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Title:Prirejanja v dvodelnih grafih
Authors:Burič, Maja (Author)
Špacapan, Simon (Mentor) More about this mentor... New window
Files:.pdf UN_Buric_Maja_2015.pdf (2,37 MB)
MD5: 50075EB6DE0CF92D22C53DCB5820F5C0
 
Language:Slovenian
Work type:Undergraduate thesis (m5)
Typology:2.11 - Undergraduate Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract: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.
Keywords:dvodelni grafi, prirejanja, pokritja, Hallov pogoj
Year of publishing:2015
Publisher:[M. Burič]
Source:Maribor
UDC:519.172.5(043.2)
COBISS_ID:21498888 New window
NUK URN:URN:SI:UM:DK:SYWBWION
Views:1010
Downloads:81
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Categories:FNM
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Secondary language

Language:English
Title:Matching in bipartite graphs
Abstract: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.
Keywords:Bipartite Graphs, matching, covering, Theorem (Hall)


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