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URN etd-0727110-000414 Author Chung-Ying Yang Author's Email Address yangcy@math.nsysu.edu.tw Statistics This thesis had been viewed 5067 times. Download 903 times. Department Applied Mathematics Year 2009 Semester 2 Degree Ph.D. Type of Document Language English Title Colouring, circular list colouring and adapted game colouring of graphs Date of Defense 2010-07-26 Page Count 96 Keyword Cartesian product chromatic number adapted game chromatic number game chromatic number circular consecutive choosability adapted consecutive choosability partial k-tree circular chromatic number planar 3-colouring circular choosability Abstract This thesis discusses colouring, circular list colouring and adapted game colouring of graphs. For colouring, this thesis obtains a sufficient condition for a planar graph to be 3-colourable. Suppose G is a planar graph. Let H_G be the graph with vertex set V (H_G) = {C : C is a cycle of G with |C| ∈ {4, 6, 7}} and edge set E(H_G) = {CiCj : Ci and Cj have edges in common}. We prove that if any 3-cycles and 5-cycles are not adjacent to i-cycles for 3 ≤ i ≤ 7, and H_G is a forest, then G is 3-colourable.

For circular consecutive choosability, this thesis obtains a basic relation among chcc(G), X(G) and Xc(G) for any finite graph G. We show that for any

finite graph G, X(G) − 1 ≤ chcc(G) < 2 Xc(G). We also determine the value of chcc(G) for complete graphs, trees, cycles, balanced complete bipartite graphs and some complete multi-partite graphs. Upper and lower bounds for chcc(G) are given for some other classes of graphs.

For adapted game chromatic number, this thesis studies the adapted game chromatic number of various classes of graphs. We prove that the maximum

adapted game chromatic number of trees is 3; the maximum adapted game chromatic number of outerplanar graphs is 5; the maximum adapted game

chromatic number of partial k-trees is between k + 2 and 2k + 1; and the

maximum adapted game chromatic number of planar graphs is between 6 and 11. We also give upper bounds for the Cartesian product of special classes of graphs, such as the Cartesian product of partial k-trees and outerplanar graphs, or planar graphs.Advisory Committee Gerard Jennhwa Chang - chair

Tung-Shan Fu - co-chair

D. J. Guan - co-chair

Sen-Peng Eu - co-chair

Zhishi Pan - co-chair

Tsai-Lien Wong - co-chair

Hong-Gwa Yeh - co-chair

Xuding Zhu - advisor

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etd-0727110-000414.pdf Date of Submission 2010-07-27