20.500.12556/DKUM-47785 Prirejanja v dvodelnih grafih Matching in bipartite graphs Diplomsko delo z naslovom Prirejanja v dvodelnih grafih je razdeljeno na tri dele.Prvo poglavje opisuje osnovne pojme v teoriji grafov. Na kratko so predstavljene tiste osnovne definicije in lastnosti grafov, ki so potrebne za lažje nadaljno razumevanje snovi. Podrobneje so obravnavani dvodelni grafi in njihove lastnosti. Dokazan je izrek, ki karakterizira dvodelne grafe kot tiste grafe, ki nimajo lihih ciklov. V drugem poglavju sta predstavljeni definiciji prirejanja in pokritija. Zapisane in slikovno ponazorjene so definicije prirejanja in pokritja, kar je pomembno za celotno obravnavo diplomskega dela. V tretjem in najpomembnejšem poglavju povežemo vso prejšnjo snov v celoto in razložimo celotno temo diplomskega dela. Dokažemo dva najpomembnejša izreka o dvodelnih grafih; Königov izrek o moči največjega prirejanja v dvodelnem grafu in Hallov izrek, ki podaja potreben in zadosten pogoj za obstoj prirejanja, ki pokrije enega izmed obeh delov dvodelne particije. Ta dva izreka sta za lažje razumevanje tudi predstavljena na primerih. Diplomsko nalogo zaključimo s posledicami, ki sledijo Hallovemu izreku in njihovimi dokazi. The graduation thesis with the title Matching in bipartite graphs is divided into three parts. The first chapter describes the basic concepts of graph theory. Briefly presents those basic definitions and properties of graphs that are needed to further facilitate the understanding of the subject. In detail are discussed bipartite graphs and their properties. It is also proven the theorem, which characterizes bipartite graphs as those graphs which have no odd cycles. The second chapter presents the concept of matching and covering. Written and illustrated are the definitions of matching and covering, which are important for the whole treatment of the thesis. The third and most important chapter rounds previous topics into whole and explains the whole topic of the thesis. We prove the two most important theorems of bipartite graphs; König theorem about the maximum cardinality of a matching in a bipartite graph and Hall's theorem, which gives a necessary and sufficient condition for the existence of matching, which satisfies one of the two parts of the dual partition. These two theorems are also presented on examples. We conclude the graduation thesis with consequences, that follow Hall's theorem and its examples. dvodelni grafi prirejanja pokritja Hallov pogoj Bipartite Graphs matching covering Theorem (Hall) true true false [M. Burič] Slovenski jezik Angleški jezik Diplomsko delo 2015-04-07 22:38:02 2015-07-23 14:04:41 2022-05-23 03:06:17 2021-05-07 03:36:19 2015 0 Maribor 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.172.5(043.2) 21498888 URN:SI:UM:DK:SYWBWION UN_Buric_Maja_2015.pdf UN_Buric_Maja_2015.pdf 1 50075EB6DE0CF92D22C53DCB5820F5C0 9a2f21bf6385ad5b9b0dd0b722d33dab3d2c6658913b7c916fd1fc1b906af2ba f0fc44c1-7c07-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=71144 Fakulteta za naravoslovje in matematiko 0 0 0