Title page for etd-0727110-000414


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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
  • Files
  • etd-0727110-000414.pdf
  • indicate access worldwide
    Date of Submission 2010-07-27

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