Multiple Coloring of Cone Graphs
學年 98
學期 1
出版（發表）日期 2010-01-01
作品名稱 Multiple Coloring of Cone Graphs
作品名稱（其他語言）
著者 Pan, Zhi-Shi; Zhu, Xu-Ding
單位 淡江大學數學學系
出版者 Philadelphia: Society for Industrial and Applied Mathematics
著錄名稱、卷期、頁數 SIAM Journal on Discrete Mathematics 24(4), pp.1515-1526
摘要 A k-fold coloring of a graph assigns to each vertex a set of k colors, and color sets assigned to adjacent vertices are disjoint. The kth chromatic number Xk(G) of a graph G is the minimum total number of colors needed in a k-fold coloring of G. Given a graph G = (V, E) and an integer m ≥ 0, the m-cone of G, denoted by µm(G), has vertex set (V x {0,1,… , m}) U {u} in which u is adjacent to every vertex of V x {m}, and (x, i)(y, j) is an edge if xy ∈ E and i = j = 0 or xy ∈ E and |i - j| = 1. This paper studies the kth chromatic number of the cone graphs. An upper bound for Xk(µm(G) in terms of Xk(G), k, and m are given. In particular, it is proved that for any graph G, if m ≥ 2k, then Xk(µm(G)) ≤ Xk(G) + 1. We also find a surprising connection between the kth chromatic number of the cone graph of G and the circular chromatic number of G. It is proved that if Xk(G)/k > Xc((G) and Xk(G) is even, then for sufficiently large m, Xk(µm(G)) = Xk(G). In particular, if X(G) > Xc(G) and X(G) is even, then for sufficiently large m, X(µm(G)) = X(G).
關鍵字 Multiple coloring; Cone graphs; Mycielski graphs; Fractional chromatic number; Kneser graphs
語言 en
ISSN 0895-4801 1095-7146‎
期刊性質 國外
收錄於 SCI
產學合作
通訊作者 Pan, Zhi-Shi; Zhu, Xu-Ding
審稿制度
國別 USA
公開徵稿
出版型式 紙本
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