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Povezavno 3-obarvljivi grafi : diplomsko delo
ID Šere, Nina (Author), ID Šparl, Primož (Mentor) More about this mentor... This link opens in a new window

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/id/eprint/4677 This link opens in a new window

Abstract
V diplomskem delu se ukvarjamo s kromatičnim indeksom kubičnih grafov, kjer se omejimo na večji del dobro znane družine takšnih grafov, znanih pod imenom posplošeni Petersenovi grafi. Graf Γ je k-povezavno obarvljiv, če se da njegove povezave obarvati s k barvami tako, da so incidenčne povezave obarvane z različnimi barvami. Najmanjše tako število k imenujemo kromatični indeks grafa in ga označimo χ'(Γ). Ker so posplošeni Petersenovi grafi kubični, ima vsak izmed njih po dobro znanem Vizingovem izreku kromatični indeks bodisi enak 3 bodisi 4. Rezultati tega diplomskega dela predstavljajo pomemben del dokaza, da je znameniti Petersenov graf edini posplošeni Petersenov graf, ki ni povezavno 3-obarvljiv. Z drugimi besedami, Petersenov graf GP(5,2) je edini posplošeni Petersenov graf s kromatičnim indeksom 4.

Language:Slovenian
Keywords:barvanje povezav, kromatični indeks, kubični graf, posplošeni Petersenov graf
Work type:Bachelor thesis/paper (mb11)
Typology:2.11 - Undergraduate Thesis
Organization:PEF - Faculty of Education
Year:2017
Publisher:[N. Šere]
Number of pages:V, 29 str.
PID:20.500.12556/RUL-95197 This link opens in a new window
UDC:519.17(043.2)
COBISS.SI-ID:11704905 This link opens in a new window
Publication date in RUL:19.09.2017
Views:834
Downloads:215
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Secondary language

Language:English
Title:3–edge colorable graphs
Abstract:
In this BSc thesis we deal with chromatic index of cubic graphs, where we mainly focus on a significant part of the family of graphs, named generalized Petersen graphs. A graph Γ is said to be k-edge-colorable, if we can color its edges with k colors, so that incident edges are colored with different colors. The smallest such number k is called the chromatic index and it is denoted by χ'(Γ). Due to the fact that generalized Petersen graphs are cubic graphs, Vizing's theorem implies that their chromatic index is either 3 or 4. The results of this BSc thesis represent an important part of the proof, that the famous Petersen graph is the only generalized Petersen graph, which is not 3-edge colorable. In other words, the Petersen graph GP(5,2) is the only generalized Petersen graph, whose chromatic index equals 4.

Keywords:mathematics, matematika

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