Barvanja grafov, ki so brez ponavljanj po licih

diplomsko delo

Sara Sabrina Zemljič (Author), Sandi Klavžar (Mentor)

Abstract

Diplomsko delo obravnava osnovne lastnosti barvanj grafov brez ponavljanj. Osrednja tema je barvanje povezav ravninskih grafov brez ponavljanj po licih. Na začetku diplomskega dela so predstavljene osnovne definicije iz teorije grafov, ki jih bomo potrebovali v nadaljevanju. V drugem poglavju vpeljemo barvanje grafov brez ponavljanj in naredimo pregled nad že znanimi rezultati o teh barvanjih. Na koncu drugega poglavja definiramo barvanje povezav ravninskih grafov brez ponavljanj po licih ter njemu pripadajoč Thuejev lični indeks, ki predstavlja najmanjše število barv, s katerimi lahko pobarvamo graf brez ponavljanj po licih. Tretje poglavje je v celoti namenjeno obravnavi barvanja dreves brez ponavljanj po licih. V tem poglavju dokažemo, da je Thuejev lični indeks dreves kvečjemu 4, kar je osnova za dokaz splošne zgornje meje Thuejevega ličnega indeksa. Na koncu pokažemo, da je Thuejev lični indeks poljubnega ravninskega grafa največ 8. Navedemo še nekaj posebnih družin ravninskih grafov, kjer se ta zgornja meja zmanjša.

Keywords

matematika;grafi;barvanje;Thuejevo število;Thuejev indeks;ravninski grafi;drevesa;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2010
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[S. S. Zemljič]
UDC:	51(043.2)
COBISS:	17859080
Views:	2117
Downloads:	171
Average score:	0 (0 votes)
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Other data

Secondary language:	English
Secondary title:	Facial non-repetitive colorings of plane graphs
Secondary abstract:	The thesis investigates basic properties of non-repetitive graph colorings. The main theme is facial non-repetitive edge coloring of planar graphs. First we present basic definitions from graph theory. In Section 2 we study non-repetitive colorings of graphs and list already known results about those colorings. At the end of Section 2 we define facial non-repetitive edge coloring of planar graphs and facial Thue index, which represents the minimum number of colors of a facial non-repetitive edge coloring of graph. The third chapter is entirely devoted to facial non-repetitive edge coloring of trees. In this section we prove that facial Thue index of a tree is at most 4, which is the basis for a proof of general upper bound on facial Thue index. Finally, we show that the facial Thue index of an arbitrary plane graph is at most 8. We also show that for some specific families of planar graphs this upper bound can be reduced.
Secondary keywords:	non-repetitive coloring;Thue number;Thue index;plane graph;tree;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	IX, 36 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	18775