Prirejanja v dvodelnih grafih

diplomsko delo

Maja Burič (Author), Simon Špacapan (Mentor)

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

diplomska dela;dvodelni grafi;prirejanje;pokritja;Hallov pogoj;

Data

Language:	Slovenian
Year of publishing:	2015
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Burič]
UDC:	519.172.5(043.2)
COBISS:	21498888
Views:	1223
Downloads:	93
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Matching in bipartite graphs
Secondary 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.
Secondary keywords:	theses;bipartite graphs;matching;covering;Hallʼs theorem;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, smer matematika in prevajanje in tolmačenje nemščina
Pages:	36 f.
ID:	8751129