### 博碩士論文 942201022 詳細資訊

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(On list coloring of graphs)

 ★ 圓環面網路上的病毒散播 ★ 以2D HP 模型對蛋白質摺疊問題之研究 ★ On Steiner centers of graphs ★ On the Steiner medians of a block graph ★ 秩為5的圖形 ★ Some results on distance-two labeling of a graph ★ 關於非奇異線圖的樹 ★ On Minimum Strictly Fundamental Cycle Basis ★ 目標集選擇問題 ★ 路徑圖與格子圖上的目標集問題 ★ 超立方體圖與格子圖上的目標集問題 ★ 圖形環著色數的若干等價定義 ★ 網格圖上有效電阻計算方法的比較 ★ d 維立方體圖上有效電阻與首達時間的計算方法

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(Congr. Numer. 26 (1979) 125-157). A new graph parameter chg,s (G) is introduced, and its nontrivial upper bound is provided which generalizes a theorem of Waters (J. London Math. Soc. 73 (2006) 565-585).In (Discrete Applied Math. 45 (1993), 277-289.), Tesman showed that if Pn is a path of n vertices then chs(Pn) = [2s(1 - 1/n)] + 1. He also
remarked that almost the same proof can be easily extended to prove that chs(Tn) = [2s(1 - 1/n)]+1 for a tree Tn of n vertices. Here we give a much shorter and neater proof for Tesman’’s result on chs(Pn) (and hence also on chs(Tn)). In (Discrete Appl. Math. 82 (1998) 1-13)Alon and Zaks proved that chs(Kn,n) = O(s log n). In this paper we present a slightly stronger version of their result. For any finite graph G, Waters (J. London Math. Soc. 73 (2006) 565-585) showed that lim{cchs(G)=s : s tends to infinity} exists, and define this limit as τ(G). In the last part of this paper, we show that there is another characterization of
τ(G), τ(G) = inf {cchs(G)=s : s belongs to N}。

Abstract (in English) ii

Contents iv
1 Introduction 1
2 Main results 3
References 10

[2] P. Erd}os, A. L. Rubin and H. Taylor, Choosability in graph, Congr.Numer. 26 (1979), 125-157.
[3] E. A. Nordhaus and J. W. Gaddum, On complementary graphs, Amer. Math. Monthly 63 (1956), 175-177.
[4] B. A. Tesman, T-colorings, list T-colorings and set T-colorings of graphs, RUTCOR Res. Rept. RRR 57-89, Rutgers University, New Brunswick, NJ (1989).
[5] B. A. Tesman, List T-colorings of graphs, Discrete Applied Math. 45(1993), 277-289.
[6] R. J. Waters, Consecutive list colouring and a new graph invariant, J. London Math. Soc. (2) 73 (2006), 565-585.