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URN etd-0125106-114359
Author Shu-yuan Lin
Author's Email Address No Public.
Statistics This thesis had been viewed 5068 times. Download 2408 times.
Department Applied Mathematics
Year 2005
Semester 1
Degree Ph.D.
Type of Document
Language English
Title Simultaneously Uniquely Circular Colourable and Uniquely Fractional Colourable Graphs
Date of Defense 2006-01-19
Page Count 65
Keyword
  • uniquely circular colourable
  • uiquely fractional colourable
  • Kneser graph
  • Abstract This thesie discusses uniquely circular colourable and uniquely fractional
    colourable graphs.
    Suppose G = (V;E) is a graph and r ¸ 2 is a real number. A circular
    r-colouring of G is a mapping f : V (G) ! [0; r) such that for any edge xy
    of G, 1 · jf(x) ¡ f(y)j · r ¡ 1. We say G is uniquely circular r-colourable
    if there is a circular r-colouring f of G and any other circular r-colouring
    of G can obtained from f by a rotation or a °ip of the colours. Let I(G)
    denote the family of independent sets of G. A fractional r-colouring of G
    is a mapping f : I(G) ! [0; 1] such that for any vertex x, Px2I f(I) = 1
    and PI2I(G) f(I) · r. A graph G is called uniquely fractional r-colourable if
    there is exactly one fractional r-colouring of G. Uniquely circular r-colourable
    graphs have been studied extensively in the literature. In particular, it is
    known that for any r ¸ 2, for any integer g, there is a uniquely circular r-
    colourable graph of girth at least g. Uniquely fractional r-colouring of graphs
    is a new concept. In this thesis, we prove that for any r ¸ 2 for any integer
    g, there is a uniquely fractional r-colourable graph of girth at least g. It is
    well-known that for any graph G, Âf (G) · Âc(G). We prove that for any
    rational numbers r ¸ r0 > 2 and any integer g, there is a graph G of girth at
    least g, which is uniquely circular r-colourable and at the same time uniquely
    fractional r0-colourable.
    Advisory Committee
  • Gerard Jenn-hwa Chang - chair
  • D. J. Guan - co-chair
  • Sen-Peng Eu - co-chair
  • Yeong-Nan Yeh - co-chair
  • Hong-Gwa Yeh - co-chair
  • Li-Da Dong - co-chair
  • Xu-ding Zhu - advisor
  • Files
  • etd-0125106-114359.pdf
  • indicate access worldwide
    Date of Submission 2006-01-25

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