### Title page for etd-0725106-232541

URN etd-0725106-232541 Yu-feng Wu m932040030@student.nsysu.edu.tw This thesis had been viewed 5182 times. Download 1808 times. Applied Mathematics 2005 2 Master English The Oriented Colourings of Bipartite Graphs 2006-07-21 24 oriented chromatic number 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 inA(D) and f(x)=f(t), then f(y)≠f(z). The oriented chromaticnumber Xo(D) of an oriented graph D is defined as the minimumk where there exists an oriented k-coloring of D. For an undirectedgraph G, let O(G) be the set of all orientations D of G. Wedefine the oriented chromatic number Xo(G) of G to be themaximum of Xo(D) over D conatined by O(G). In this thesis, wedetermine the oriented chromatic number of complete bipartite graphs andcomplete k-partite graphs. A grid G(m,n) is a graph with thevertex set V(G(m,n))={(i,j) | 1≦i≦m,1≦j≦n} and the edgeset 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 ofXo(D(5,6)=7 where D(5,6) is the orientation ofG(5,6). none - chair none - co-chair none - co-chair none - co-chair Li-Da Tong - advisor indicate accessible in a year 2006-07-25

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