Title page for etd-0725106-232541


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URN etd-0725106-232541
Author Yu-feng Wu
Author's Email Address m932040030@student.nsysu.edu.tw
Statistics This thesis had been viewed 5067 times. Download 1719 times.
Department Applied Mathematics
Year 2005
Semester 2
Degree Master
Type of Document
Language English
Title The Oriented Colourings of Bipartite Graphs
Date of Defense 2006-07-21
Page Count 24
Keyword
  • oriented chromatic number
  • Abstract Let S be a set of k distinct elements. An oriented k coloring of an oriented graph D is a mapping f:V(D)→S such that (i) if xy is conatined in A(D), then f(x)≠f(y) and (ii) if xy,zt are conatined in
    A(D) and f(x)=f(t), then f(y)≠f(z). The oriented chromatic
    number Xo(D) of an oriented graph D is defined as the minimum
    k where there exists an oriented k-coloring of D. For an undirected
    graph G, let O(G) be the set of all orientations D of G. We
    define the oriented chromatic number Xo(G) of G to be the
    maximum of Xo(D) over D conatined by O(G). In this thesis, we
    determine the oriented chromatic number of complete bipartite graphs and
    complete k-partite graphs. A grid G(m,n) is a graph with the
    vertex set V(G(m,n))={(i,j) | 1≦i≦m,1≦j≦n} and the edge
    set E(G(m,n))={(i,j)(x,y) | (i=x+1 and j=y) or (i=x and j=y+1)}. Fertin, Raspaud and Roychowdhury [3] proved Xo(G(4,5))≧7 by computer programs. Here, we give a proof of
    Xo(D(5,6)=7 where D(5,6) is the orientation of
    G(5,6).
    Advisory Committee
  • none - chair
  • none - co-chair
  • none - co-chair
  • none - co-chair
  • Li-Da Tong - advisor
  • Files
  • etd-0725106-232541.pdf
  • indicate accessible in a year
    Date of Submission 2006-07-25

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