{"id":279,"date":"2019-09-12T14:43:21","date_gmt":"2019-09-12T12:43:21","guid":{"rendered":"http:\/\/www4.ekf.tuke.sk\/kamahi\/?page_id=279"},"modified":"2025-11-10T13:44:22","modified_gmt":"2025-11-10T12:44:22","slug":"julius-czap","status":"publish","type":"page","link":"https:\/\/kamahi.ekf.tuke.sk\/index.php\/julius-czap\/","title":{"rendered":"J\u00falius Czap"},"content":{"rendered":"\n<style type=\"text\/css\">\n.entry-content table,\n.entry-content th,\n.entry-content tr,\n.entry-content td{\n\tborder:none;\n}\ntable.other,\ntd.other,\ntr.other{\n\tpadding: 5px 5px 5px;\n}\ntable.other,\ntd.other,\ntr.other{\nborder: 1px solid black;\n}\n<\/style>\n\n<table style=\"float: left; width: 950px\">\n<tr>\n<td align=\"right\"><h4><a href=\"#experience\" target=\"_self\" class=\"btn-secondary\" rel=\"noopener noreferrer\">Pedagogick\u00e1 \u010dinnos\u0165<\/a><\/h4><\/td>\n<td align=\"center\"><h4><a href=\"#work\" target=\"_self\" class=\"btn-secondary\" rel=\"noopener noreferrer\">Publik\u00e1cie<\/a><\/h4><\/td>\n<td align=\"center\"><h4><a href=\"#project\" target=\"_self\" class=\"btn-secondary\" rel=\"noopener noreferrer\">Projekty<\/a><\/h4><\/td>\n<td align=\"left\"><h4><a href=\"#contact\" target=\"_self\" class=\"btn-secondary\" rel=\"noopener noreferrer\">Kontakt<\/a><\/h4><\/td>\n<tr>\n<\/table>\n\n\n\n<img decoding=\"async\" style=\"width: 250px; float: right\" class=\"wp-image-364\" src=\"https:\/\/kamahi.ekf.tuke.sk\/wp-content\/uploads\/2019\/10\/EkF-zamestnanci-011.jpg\" alt=\"jc\">\n\n<div style=\"float: left; width: 75%\"><p align=\"left\"> \n<h4><a name=\"experience\">Pedagogick\u00e1 \u010dinnos\u0165<\/a><\/h4>\n<p><span style=\"text-decoration: underline;\"><strong>Cvi\u010denia:<\/strong><\/span><\/p>\n<ul>\n<li>Aplikovan&aacute; te&oacute;ria grafov v ekon&oacute;mii<\/li>\n<li>Matematika I<\/li>\n<li>Matematika II<\/li>\n<\/ul>\n<p><span style=\"text-decoration: underline;\"><strong>Predn\u00e1\u0161ky:<\/strong><\/span><\/p>\n<ul>\n<li>Aplikovan&aacute; te&oacute;ria grafov v ekon&oacute;mii<\/li>\n<\/ul>\n<p><span style=\"text-decoration: underline;\"><strong>Konzulta\u010dn\u00e9 hodiny<\/strong><\/span><\/p>\n<ul>\n<li>po dohode &#8211; julius.czap@tuke.sk<\/li>\n<\/ul>\n\n<p><b>Vedenie z\u00e1vere\u010dn\u00fdch pr\u00e1c<\/b><\/p>\n<p><span style=\"text-decoration: underline;\"><strong>Diplomov\u00e9 pr\u00e1ce:<\/strong><\/span><\/p>\n<ul>\n<li>Optimaliz&aacute;cia intern&eacute;ho finan\u010dn&eacute;ho reportingu v korpor&aacute;tnej sf&eacute;re s vyu\u017eit&iacute;m prostriedkov automatiz&aacute;cie (2018\/2019 FBI)<\/li>\n<li>N&aacute;vrh tvorby portf&oacute;lia a anal&yacute;za jeho v&yacute;konnosti (2016\/2017 FBI)<\/li>\n<li>Ekonomick&eacute; a bezpe\u010dnostn&eacute; aspekty zav&aacute;dzania bezkontaktnej technol&oacute;gie (2016\/2017 FBI)<\/li>\n<li>Vyu\u017e&iacute;vanie Smart bankingu v podmienkach SR (2016\/2017 FBI)<\/li>\n<li>Webov&eacute; rozhranie pre demon&scaron;tr&aacute;ciu grafov a grafov&yacute;ch algoritmov &#8211; cesty (2012\/2013 HI)<\/li>\n<\/ul>\n\n<p><span style=\"text-decoration: underline;\"><strong>Bakal&aacute;rske pr&aacute;ce:<\/strong><\/span><\/p>\n<ul>\n<li> Hypot\u00e9ka na vlastn\u00e9 b\u00fdvanie alebo podn\u00e1jom? (2023\/2024 FBI)<\/li>\n<li> Invest\u00edcie do nehnute\u013enost\u00ed &#8211; finan\u010dn\u00e1 n\u00e1vratnos\u0165 (2023\/2024 EaMVS)<\/li>\n<li> Mo\u017enosti sporenia pre priemerne zar\u00e1baj\u00facich v SR (2023\/2024 FBI)<\/li>\n<li> Trh elektromobilov na Slovensku a v zahrani\u010d\u00ed (2023\/2024 FBI)<\/li>\n\n<li> Diverzifik\u00e1cia rizika pri investovan\u00ed (2021\/2022 FBI)<\/li>\n<li> Finan\u010dn\u00e9 riadenie futbalov\u00e9ho klubu (2021\/2022 FBI)<\/li>\n\n<li> Modely sporenia na Slovensku (2018\/2019 FBI)<\/li>\n\n<li> Finan\u010dn&aacute; gramotnos\u0165 &scaron;tudentov (2017\/2018 FBI)<\/li>\n<li> Obnova budov a n&aacute;vratnos\u0165 invest&iacute;ci&iacute; (2017\/2018 FBI)<\/li>\n\n<li> Financovanie b&yacute;vania (2016\/2017 FBI)<\/li>\n<li> Modelovanie medzin&aacute;rodn&eacute;ho obchodu (2016\/2017 FBI)<\/li>\n<li> Stabilita na finan\u010dn&yacute;ch trhoch (2016\/2017 FBI)<\/li>\n<li> Trh nehnute\u013enost&iacute; v Ko&scaron;iciach (2016\/2017 FBI)<\/li>\n<li> Vyu\u017eitie met&oacute;dy kritickej cesty vo v&yacute;robn&yacute;ch procesoch (2016\/2017 EaMVS)<\/li>\n<li> Vz\u0165ahy v soci&aacute;lnych sie\u0165ach (2016\/2017 FBI)<\/li>\n\n<li> Trh telekomunika\u010dn&yacute;ch oper&aacute;torov na Slovensku (2015\/2016 FBI)<\/li>\n\n<li> Najv&yacute;hodnej&scaron;&iacute; sp&ocirc;sob prepravy tovaru (2014\/2015 FBI)<\/li>\n<li> Optimaliz&aacute;cia rozdelenia pr&aacute;c medzi zamestnancami(2014\/2015 FBI)<\/li>\n<li> Rozhodovac&iacute; probl&eacute;m pri preprave u\u017eito\u010dn&yacute;ch predmetov (2014\/2015 FBI)<\/li>\n\n<li> Aplik&aacute;cie te&oacute;rie grafov &ndash; v&yacute;u\u010dbov&eacute; moduly v LMS Moodle (2013\/2014 HI)<\/li>\n<li> Obchodovanie na menovej burze Forex pomocou automatick&yacute;ch obchodn&yacute;ch syst&eacute;mov (2013\/2014 HI)<\/li>\n<li> On-line v&yacute;u\u010dbov&eacute; materi&aacute;ly pre predmet Te&oacute;ria grafov (2013\/2014 HI)<\/li>\n\n<li>V&yacute;u\u010dbov&eacute; moduly v LMS Moodle &#8211; Te&oacute;ria grafov (2012\/2013 HI)<\/li>\n\n<li> Dopravn&eacute; &uacute;lohy &#8211; preprava tovaru za najni\u017e&scaron;iu cenu (2011\/2012 HI)<\/li>\n<li>Obsadzovanie nehnute\u013enosti v danej lokalite prostredn&iacute;ctvom webovej aplik&aacute;cie (2011\/2012 HI)<\/li>\n\n<\/ul>\n<\/div>\n\n\n\n\n\n<!--\n<h4><a name=\"work\">Publik\u00e1cie<\/a><\/h4>\n<h5>5 najv\u00fdznamnej\u0161\u00edch publik\u00e1cii<\/h5>\n<ul align=\"justify\">\n<table class=\"other\">\n<tbody>\n<tr class=\"other\">\n<td class=\"other\" width=\"7%\"><strong>Kateg\u00f3ria<\/strong><\/td>\n<td class=\"other\"><strong>Publik\u00e1cia<\/strong><\/td>\n<\/tr>\n<tr class=\"other\">\n<td class=\"other\"><strong>???<\/strong><\/td>\n<td class=\"other\">???<\/td>\n<\/tr>\n<tr class=\"other\">\n<td class=\"other\"><strong>???<\/strong><\/td>\n<td class=\"other\">???<\/td>\n<\/tr>\n<tr class=\"other\">\n<td class=\"other\"><strong>???<\/strong><\/td>\n<td class=\"other\">???<\/td>\n<\/tr>\n<tr class=\"other\">\n<td class=\"other\"><strong>???<\/strong><\/td>\n<td class=\"other\">???<\/td>\n<\/tr>\n<tr class=\"other\">\n<td class=\"other\"><strong>???<\/strong><\/td>\n<td class=\"other\">???<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/ul>\n<li><a href=\"https:\/\/epc.lib.tuke.sk\/EvidPublQ.aspx?rok=9999&priezv=Czap&meno=Julius\" target=\"_blank\" rel=\"noopener noreferrer\">Zoznam v\u0161etk\u00fdch publik\u00e1ci\u00ed<\/a><\/li>\n<\/ul>\n-->\n\n\n\n\n\n<h4><a name=\"work\">Publik\u00e1cie<\/a><\/h4>\n\n<ol align=\"justify\">\n\n<li><strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"https:\/\/shahindp.com\/Contrib_Math\/v12\/CM25_v12_pp25-30.pdf\">Even facial 2-colorings of plane graphs<\/a><\/em>, Contributions to Mathematics 12 (2025) 25&nbsp;&ndash; 30.<\/span> <\/li>\n\n\n<li><strong><span> J. Czap<\/span><\/strong>, S. Jendro\u013e, P. \u0160ugerek:<em> <a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=2545\">On P vertex-connections of graphs<\/a><\/em>, Discussiones  Mathematicae Graph Theory 45 (2) (2025) 637&nbsp;&ndash; 652.<\/li>\n\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e: <em><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0166218X24005341\">Facial matchings in plane graphs<\/a><\/em>, Discrete Applied Mathematics 364 (2025) 16&nbsp;&ndash; 22. <\/span><\/li>\n\n<li><strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"https:\/\/www.opuscula.agh.edu.pl\/vol44\/6\/art\/opuscula_math_4438.pdf\">Facial graceful coloring of plane graphs<\/a><\/em>, Opuscula Mathematica 44 (6) (2024) 815&nbsp;&ndash; 825.<\/span> <\/li>\n\n<li><strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"https:\/\/shahindp.com\/Contrib_Math\/v10\/CM24_v10_pp20-24.pdf\">Odd facial total-coloring of maximal plane and outerplane graphs<\/a><\/em>, Contributions to Mathematics 10 (2024) 20&nbsp;&ndash; 24.<\/span> <\/li>\n\n<li><strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"https:\/\/www.dmlett.com\/archive\/v12\/DML23_v12_pp73-77.pdf\">Rainbow subgraphs in edge-colored planar and outerplanar graphs<\/a><\/em>, Discrete Mathematics Letters 12 (2023) 73&nbsp;&ndash; 77.<\/span> <\/li>\n\n<li><strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"http:\/\/comb-opt.azaruniv.ac.ir\/article_14458_5845ed2278653c2ca1ef0b462e225152.pdf\">A note on odd facial total-coloring of cacti<\/a><\/em>, Communications in Combinatorics and Optimization 8 (3) (2023) 589&nbsp;&ndash; 594.<\/span> <\/li>\n\n<li><strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"https:\/\/www.dmlett.com\/archive\/v10\/DML22_v10_pp56-59.pdf\">Odd facial total-coloring of unicyclic plane graphs<\/a><\/em>, Discrete Mathematics Letters 10 (2022) 56&nbsp;&ndash; 59.<\/span> <\/li>\n\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, T. Madaras: <em><a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00373-021-02411-9\">Facial visibility in edge colored plane graphs<\/a><\/em>, Graphs and Combintorics 38 (2022) 4.<\/span> <\/li>\n\n<li><strong><span> J. Czap<\/span><\/strong><span>, P. \u0160ugerek: <em><a href=\"https:\/\/www.ejgta.org\/index.php\/ejgta\/article\/view\/775\">Odd facial colorings of acyclic plane graphs<\/a><\/em>, Electronic Journal of Graph Theory and Applications 9 (2) (2021) 347&nbsp;&ndash; 355.<\/span> <\/li>\n\n<li><strong><span> J. Czap<\/span><\/strong><span>, I. Fabrici, S. Jendro\u013e: <em><a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=2319\">Colorings of plane graphs without long monochromatic facial paths<\/a><\/em>, Discussiones  Mathematicae Graph Theory 41 (3) (2021) 801&nbsp;&ndash; 808.<\/span> <\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, M. Hor\u0148\u00e1k, S. Jendro\u013e: <em><a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=2369\">A survey on the cyclic coloring and its relaxations<\/a><\/em>, Discussiones  Mathematicae Graph Theory 41 (1) (2021) 5&nbsp;&ndash; 38.<\/span> <\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, J. Valiska: <em><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0166218X19305104\">Edge-coloring of plane multigraphs with many colors on facial cycles<\/a><\/em>, Discrete Applied Mathematics 282 (2020) 80&nbsp;&ndash; 85.<\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"https:\/\/www.opuscula.agh.edu.pl\/vol40\/4\/art\/opuscula_math_4025.pdf\">Facial rainbow edge-coloring of simple 3-connected plane graphs<\/a><\/em>, Opuscula Mathematica 40 (4) (2020) 475&nbsp;&ndash; 482.<\/span><\/li>\n<!--\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, J. Valiska: <em><a href=\"http:\/\/www.iam.fmph.uniba.sk\/amuc\/ojs\/index.php\/amuc\/article\/view\/1185\/696\">Edge-coloring of plane graphs with many colors on faces<\/a><\/em>, Acta Mathematica Universitatis Comenianae 88 (3) (2019) 573&nbsp;&ndash; 576.<\/span><\/li>\n -->\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e: <em><a href=\"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219265919400036\">Facial colorings of plane graphs<\/a><\/em>, Journal of Interconnection Networks 19 (1) (2019) 1940003.<\/span> <\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, P. &Scaron;ugerek, J. Valiska: <em><a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=2135\">Facial [r,s,t]-colorings of plane graphs<\/a><\/em>, Discussiones  Mathematicae Graph Theory 39 (3) (2019) 629&nbsp;&ndash; 645.<\/span> <\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, P. &Scaron;ugerek, J. Valiska: <em><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0166218X18305699\">Facial packing vertex-coloring of subdivided plane graphs<\/a><\/em>, Discrete Applied Mathematics 257 (2019) 95&nbsp;&ndash; 100.<\/span> <\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, J. Valiska: <em><a href=\"https:\/\/www.sciencedirect.com\/science\/article\/pii\/S0166218X18301896\">Facial L(2,1)-edge-labelings of trees<\/a><\/em>, Discrete Applied Mathematics 247 (2018) 357&nbsp;&ndash; 366.<\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, M. Voigt: <em><a href=\"http:\/\/www.opuscula.agh.edu.pl\/vol38\/6\/art\/opuscula_math_3837.pdf\">Zig-zag facial total-coloring of plane graphs<\/a><\/em>, Opuscula Mathematica 38 (6) (2018) 819 &ndash; 827.<\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, J. Valiska: <em><a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=2036\">Conflict-free connections of graphs<\/a><\/em>, Discussiones  Mathematicae Graph Theory 38 (4) (2018) 911 &ndash; 920.<\/span><\/li>\n<li>J. Bucko, <strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"https:\/\/ijpam.eu\/contents\/2017-117-1\/18\/18.pdf\">Another step towards determining the hit number of subdivided stars<\/a><\/em>, International Journal of Pure and Applied Mathematics 117 (1) (2017) 247&nbsp;&ndash; 254.<\/span><\/li>\n<li><strong>J. Czap<\/strong>, S. Jendro\u013e: <em><a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0012365X16302576\">Facially-constrained colorings of plane graphs: A survey<\/a><\/em>, Discrete Mathematics  340 (2017) 2691&nbsp;&ndash; 2703.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, R. Sot&aacute;k: <em><a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0166218X17303049\">Facial anagram-free edge-coloring of plane graphs<\/a><\/em>, Discrete Applied Mathematics 230 (2017) 151&nbsp;&ndash; 155. <\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, P. &Scaron;ugerek: <em><a href=\"http:\/\/www.ijpam.eu\/contents\/2017-115-1\/9\/9.pdf\">Facial total-coloring of bipartite plane graphs<\/a><\/em>, International Journal of Pure and Applied Mathematics 115 (1) (2017) 115&nbsp;&ndash; 121.<\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, J. Valiska: <em><a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=1921\">WORM colorings of plane graphs<\/a><\/em>, Discussiones  Mathematicae Graph Theory 37 (2) (2017) 353&nbsp;&ndash; 368.<\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong>, P. &Scaron;ugerek:<em> <a href=\"http:\/\/journal.pmf.ni.ac.rs\/filomat\/index.php\/filomat\/article\/view\/2057\/1698\">Drawing graph joins in the plane with restrictions on crossings<\/a><\/em>, Filomat 31 (2) (2017) 363&nbsp;&ndash; 370.<\/li>\n<li>J. Bucko, <strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"http:\/\/www.m-hikari.com\/ams\/ams-2016\/ams-49-52-2016\/p\/czapAMS49-52-2016.pdf\">Structural theorem in 3-polytopes with minimum degree five<\/a><\/em>, Applied Mathematical Sciences 10 (49) (2016) 2437&nbsp;&ndash; 2442. <\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e: <em><a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0166218X1630227X\">Facial packing edge-coloring of plane graphs<\/a><\/em>, Discrete Applied Mathematics 213 (2016) 71&nbsp;&ndash; 75. <\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, J. Przyby\u0142o, E. &Scaron;krabul&#8217;&aacute;kov&aacute;: <em><a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=1845\">On an extremal problem in the class of bipartite 1-planar graphs<\/a><\/em>, Discussiones  Mathematicae Graph Theory 36 (1) (2016) 59&nbsp;&ndash; 69. <\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, J. Ivan\u010do, P. &Scaron;ugerek: <em><a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=1842\">M2-edge colorings of cacti and graph joins<\/a><\/em>, Discussiones  Mathematicae Graph Theory 36 (1) (2016) 141&nbsp;&ndash; 151. <\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"https:\/\/amc-journal.eu\/index.php\/amc\/article\/view\/609\/833\">Edge looseness of plane graphs<\/a><\/em>, Ars Mathematica Contemporanea 9 (2) (2015) 289&nbsp;&ndash;&nbsp;296<\/span><span>.<\/span><\/li>\n<li>J. Bucko, <strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"http:\/\/www.m-hikari.com\/ams\/ams-2015\/ams-109-112-2015\/p\/czapAMS109-112-2015.pdf\">1-planar lexicographic products of graphs<\/a><\/em>, Applied Mathematical Sciences 9 (109) (2015) 5441&nbsp;&ndash; 5449. <\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e: <em><a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0166218X15002346\">Facial edge ranking of plane graphs<\/a><\/em>, Discrete Applied Mathematics 194 (2015) 60&nbsp;&ndash; 64. <\/span><\/li>\n<li>T. B&aacute;lint, <strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"http:\/\/link.springer.com\/article\/10.1007\/s00373-014-1472-7\">Facial parity 9-edge-coloring of outerplane graphs<\/a><\/em>, Graphs and Combinatorics 31 (5) (2015) 1177&nbsp;&ndash; 1187. <\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong>, P. &Scaron;ugerek:<em> <a href=\"http:\/\/www.m-hikari.com\/ams\/ams-2015\/ams-77-80-2015\/p\/czapAMS77-80-2015.pdf\">Mi-edge colorings of complete graphs<\/a><\/em>, Applied Mathematical Sciences 9 (77) (2015) 3835&nbsp;&ndash; 3842.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong>:<em> <a href=\"https:\/\/www.opuscula.agh.edu.pl\/vol35\/3\/art\/opuscula_math_3519.pdf\">A note on M2-edge colorings of graphs<\/a><\/em>, Opuscula Mathematica 35 (3) (2015) 287&nbsp;&ndash; 291.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong>, P. Hud&aacute;k, T. Madaras:<em> <a href=\"https:\/\/link.springer.com\/article\/10.1007\/s10114-014-4017-3\">Joins of 1-planar graphs<\/a><\/em>, Acta Mathematica Sinica, English Series 30 (11) (2014) 1867&nbsp;&ndash; 1876.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong>, P. &Scaron;ugerek:<em> <a href=\"http:\/\/www.m-hikari.com\/ams\/ams-2014\/ams-93-96-2014\/czapAMS93-96-2014.pdf\">Face-distinguishing facially-proper entire-labeling of plane graphs<\/a><\/em>, Applied Mathematical Sciences 8 (96) (2014) 4767&nbsp;&ndash; 4774.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong>, J. Harant, D. Hud&aacute;k:<em> <a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0166218X12004258\">An upper bound on the sum of powers of the degrees of simple 1-planar graphs<\/a><\/em>, Discrete Applied Mathematics 165 (2014) 146&nbsp;&ndash; 151. <\/li>\n<li>K. Budajov&aacute;, <strong><span> J. Czap<\/span><\/strong>:<em> <a href=\"http:\/\/www.ijpam.eu\/contents\/2013-88-2\/1\/1.pdf\">M2-edge coloring and maximum matching of graphs<\/a><\/em>, International Journal of Pure and Applied Mathematics 88 (2) (2013) 161&nbsp;&ndash; 167.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, Zs. Tuza: <em><a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=1690\">Decompositions of plane graphs under parity constrains given by faces<\/a><\/em>, Discussiones  Mathematicae Graph Theory 33 (3) (2013) 521&nbsp;&ndash; 530. <\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, P. Mih&oacute;k: <em><a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=1685\">Fractional Q-coloring of graphs<\/a><\/em>, Discussiones  Mathematicae Graph Theory 33 (3) (2013) 509&nbsp;&ndash; 519. <\/span><\/li>\n<li>J. Bar&aacute;t, <strong><span> J. Czap<\/span><\/strong>:<em> <a href=\"http:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.21695\/pdf\">Facial nonrepetitive vertex coloring of plane graphs<\/a><\/em>, Journal of Graph Theory 74 (1) (2013) 115&nbsp;&ndash; 121.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong>, D. Hud&aacute;k:<em> <a href=\"http:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i2p54\/pdf\">On drawings and decompositions of 1-planar graphs<\/a><\/em>, The Electronic Journal of Combinatorics  20 (2) (2013) #P54. <\/li>\n<li>K. Budajov&aacute;, <strong><span> J. Czap<\/span><\/strong>:<em> <a href=\"http:\/\/www.ijpam.eu\/contents\/2013-85-1\/11\/11.pdf\">Facial r-acyclic edge-colorings of plane graphs<\/a><\/em>, International Journal of Pure and Applied Mathematics 85 (1) (2013) 141&nbsp;&ndash; 147.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong>:<em> <a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0020019013001208\">A note on total colorings of 1-planar graphs<\/a><\/em>, Information Processing Letters 113 (14-16) (2013) 516&nbsp;&ndash; 517.<\/li>\n<li>K. Budajov&aacute;, <strong><span> J. Czap<\/span><\/strong>:<em> <a href=\"http:\/\/www.m-hikari.com\/ams\/ams-2012\/ams-133-136-2012\/czapAMS133-136-2012.pdf\">Hit number of sparse subdivided stars<\/a><\/em>, Applied Mathematical Sciences 6 (136) (2012) 6753&nbsp;&ndash; 6759.<\/li>\n<li>K. Budajov&aacute;, <strong><span> J. Czap<\/span><\/strong>:<em> <a href=\"http:\/\/www.m-hikari.com\/ams\/ams-2012\/ams-113-116-2012\/czapAMS113-116-2012.pdf\">Hit number of directed bipartite graphs<\/a><\/em>, Applied Mathematical Sciences 6 (114) (2012) 5689&nbsp;&ndash; 5693.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, F. Kardo&scaron;, and R. Sot&aacute;k: <em><a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0012365X12001598\">Facial parity edge colouring of plane pseudographs<\/a><\/em>, Discrete Mathematics 312 (17) (2012) 2735&nbsp;&ndash;&nbsp;2740<\/span><span>.<\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>: <em><a href=\"https:\/\/amc-journal.eu\/index.php\/amc\/article\/view\/228\/169\">Facial parity edge coloring of outerplane graphs<\/a><\/em>, Ars Mathematica Contemporanea 5 (2) (2012) 285&nbsp;&ndash;&nbsp;289<\/span><span>.<\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong>, D. Hud&aacute;k:<em> <a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0166218X11004641\">1-planarity of complete multipartite graphs<\/a><\/em>, Discrete Applied Mathematics 160 (4-5) (2012) 505 &ndash; 512. <\/li>\n<li><strong><span> J. Czap<\/span><\/strong>:<em> <a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0012365X11002664\">Parity vertex colouring of outerplane graphs<\/a><\/em>, Discrete Mathematics 311 (21) (2011) 2570&nbsp;&ndash; 2573.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong>:<em> <a href=\"http:\/\/www.m-hikari.com\/ams\/ams-2011\/ams-49-52-2011\/czapAMS49-52-2011.pdf\">Mi-edge colorings of graphs<\/a><\/em>, Applied Mathematical Sciences 5 (49) (2011) 2437&nbsp;&ndash; 2442.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong>, S. Jendro\u013e, and M. Voigt:<em> <a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0012365X10004620\">Parity vertex colouring of plane graphs<\/a><\/em>, Discrete Mathematics 311 (6) (2011) 512&nbsp;&ndash; 520.<\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, and F. Kardo&scaron;: <em><a href=\"https:\/\/amc-journal.eu\/index.php\/amc\/article\/view\/129\/135\">Facial parity edge colouring<\/a><\/em>, Ars Mathematica Contemporanea 4 (2) (2011) 255&nbsp;&ndash;&nbsp;269<\/span><span>.<\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, and F. Kardo&scaron;: <em><a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=1567\">On the strong parity chromatic number<\/a><\/em>, Discussiones  Mathematicae Graph Theory 31 (3) (2011) 587 &ndash; 600<\/span><span>. <\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong><span>, S. Jendro\u013e, F. Kardo&scaron;, and J. Mi&scaron;kuf: <em><a href=\"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00373-010-0961-6\">Looseness      of plane graphs<\/a><\/em>, Graphs and Combinatorics 27 (1) (2011) 73&nbsp;&ndash;&nbsp;85.<\/span><\/li>\n<li><strong><span> J. Czap<\/span><\/strong>, S. Jendro\u013e:<em> <a href=\"https:\/\/www.dmgt.uz.zgora.pl\/publish\/pdf.php?doi=1462\">Colouring vertices of plane graphs under restrictions given by faces<\/a><\/em>, Discussiones  Mathematicae Graph Theory 29 (3) (2009) 521 &ndash; 543. <\/li>\n<\/ol>\n\n<h4><a name=\"project\">Projekty<\/a><\/h4>\n<p>\n<li><span> APVV-23-0191, <em> Farebnos\u0165 a \u0161trukt\u00fara plan\u00e1rnych, vnoren\u00fdch a plan\u00e1rno-pr\u00edbuzn\u00fdch grafov<\/em>, 2024 &ndash; 2028<\/span><\/li>\n<li><span> APVV-19-0153, <em>Vnoren\u00e9 grafy &#8211; zafarbenia a \u0161trukt\u00fara<\/em>, 2020 &ndash; 2024<\/span><\/li>\n<li><span> APVV-15-0116, <em>&Scaron;truktur&aacute;lne a chromatick&eacute; charakteristiky grafov<\/em>, 2016 &ndash; 2020<\/span><\/li>\n<li><span> APVV-0007-07, <em>Vnorenia, zafarbenia a&nbsp;ohodnotenia grafov<\/em>, 2008 &ndash; 2010<\/span><\/li>\n<li><span> VEGA 1\/0201\/19, <em>Syst&eacute;my pre podporu rozhodovania a business intelligence v r&aacute;mci sie\u0165ovej ekonomiky<\/em>, 2019 &ndash; 2021<\/span><\/li>\n<li><span> VEGA 1\/0945\/12, <em>Modely bezpe\u010dnosti distribuovan&yacute;ch syst&eacute;mov poskytuj&uacute;cich elektronick&eacute; slu\u017eby<\/em>, 2012 &ndash; 2013<\/span><\/li>\n<li><span> VEGA 1\/1042\/12, <em>Reakcie akciov&yacute;ch trhov na invest&iacute;cie do informa\u010dn&yacute;ch a komunika\u010dn&yacute;ch technol&oacute;gi&iacute; na pr&iacute;klade trhov v krajin&aacute;ch Vy&scaron;ehradskej &scaron;tvorky<\/em>, 2012 &ndash; 2013<\/span><\/li>\n<li><span> VEGA 1\/3004\/06, <em>&Scaron;trukt&uacute;ra, vnorenia, zafarbenia a&nbsp;ohodnotenia grafov<\/em>, 2006 &ndash; 2008<\/span><\/li>\n<\/p>\n\n<h4><a name=\"contact\">Kontakt<\/a><\/h4>\n<table>\n<tr>\n<td><b>Adresa<\/b><\/td>\n<td><b>Kancel\u00e1ria<\/b><\/td>\n<td><b>Telef\u00f3n<\/b><\/td>\n<td><b>E-mail<\/b><\/td>\n<tr>\n\n<tr>\n<td>Technick\u00e1 univerzita v Ko\u0161iciach<p>N\u011bmcovej 32, 040 01  Ko\u0161ice<\/td>\n<td>\u010c\u00edslo dver\u00ed: 212<\/td>\n<td>055\/602 3273<\/td>\n<td>julius.czap@tuke.sk<\/td>\n<tr>\n<\/table>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pedagogick\u00e1 \u010dinnos\u0165 Publik\u00e1cie Projekty Kontakt Pedagogick\u00e1 \u010dinnos\u0165 Cvi\u010denia: Aplikovan&aacute; te&oacute;ria grafov v ekon&oacute;mii Matematika I Matematika II Predn\u00e1\u0161ky: Aplikovan&aacute; te&oacute;ria grafov v ekon&oacute;mii Konzulta\u010dn\u00e9 hodiny&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-279","page","type-page","status-publish","hentry","no-post-thumbnail"],"_links":{"self":[{"href":"https:\/\/kamahi.ekf.tuke.sk\/index.php\/wp-json\/wp\/v2\/pages\/279"}],"collection":[{"href":"https:\/\/kamahi.ekf.tuke.sk\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/kamahi.ekf.tuke.sk\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/kamahi.ekf.tuke.sk\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kamahi.ekf.tuke.sk\/index.php\/wp-json\/wp\/v2\/comments?post=279"}],"version-history":[{"count":144,"href":"https:\/\/kamahi.ekf.tuke.sk\/index.php\/wp-json\/wp\/v2\/pages\/279\/revisions"}],"predecessor-version":[{"id":3976,"href":"https:\/\/kamahi.ekf.tuke.sk\/index.php\/wp-json\/wp\/v2\/pages\/279\/revisions\/3976"}],"wp:attachment":[{"href":"https:\/\/kamahi.ekf.tuke.sk\/index.php\/wp-json\/wp\/v2\/media?parent=279"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}