20.500.12556/DKUM-60226 Hedeniemijeva domneva in retrakti produktnih grafov Hedetniemi's conjecture and the retracts of a product of graphs Osrednji del diplomskega dela predstavljata Hedetniemijeva domneva in retrakti grafov. V delu je obravnavan pojem homomorfizmov med grafi, to je preslikava med grafi, ki ohranja povezave, ter kombinatorična struktura direktnih grafovskih produktov. Uvodno poglavje je namenjeno pregledu osnovnih pojmov, ki izhajajo s področja teorije grafov in teorije grup. Nato so bolj podrobno obravnavane preslikave med grafi, kromatično število grafa, retrakt in jedro grafa. V nadaljevanju je predstavljena Hedetniemijeva domneva in njene ekvivalentne trditve. Predstavljena je trditev, ki povezuje retrakt produktnega grafa z osrednjo domnevo. The central part of the thesis focusses on Hedetniemi’s Conjecture and the Retracts of a Product of Graphs. The thesis discusses the concept of homomorphism’s among graphs, this mapping preserves the edges between the graphs. Combinatorial structure of the direct product is also discussed. The introductory chapter is devoted to a basic review of the theory of graphs, as well as group theory. More detail on mapping between graphs, chromatic number, retract, and core graph is discussed in subsequent chapters. The thesis continues with the introduction of Hedetniemi’s conjecture and its equivalent statements. It also presents an theorem that connects the retracts of a product graphs with the central conjectuere. Hedetniemijeva domneva produktni graf retrakt grafa jedro grafa homomorfizem grafa kromatično število. Hedetniemi’s conjecture product of graphs retract of a graph core graph homomorphism cromatic number. true true false [A. Bezjak] Slovenski jezik Angleški jezik Diplomsko delo 2016-06-09 21:37:26 2016-09-09 12:38:19 2023-09-26 09:03:27 2019-07-11 11:39:25 2016 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.17(043.2) 22507784 URN:SI:UM:DK:7ATQIJCO UN_Bezjak_Alenka_2016.pdf UN_Bezjak_Alenka_2016.pdf 1 9664DC49CD099E539AB2037D7F8F7A45 3ad8b9980c797b95a959cb6289253b507807d24f24a7c0323fb7cb7c37aeab99 ac94f02d-7c0c-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=94109 Fakulteta za naravoslovje in matematiko 0 0 0