Results on the Grundy chromatic number of graphs
نویسندگان
چکیده
منابع مشابه
Results on the Grundy chromatic number of graphs
Given a graph G, by a Grundy k-coloring of G we mean any proper k-vertex coloring of G such that for each two colors i and j, i < j , every vertex ofG colored by j has a neighbor with color i. The maximum k for which there exists a Grundy k-coloring is denoted by (G) and called Grundy (chromatic) number of G. We first discuss the fixed-parameter complexity of determining (G) k, for any fixed in...
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A Grundy k-coloring of a graph G, is a vertex k-coloring of G such that for each two colors i and j with i < j, every vertex of G colored by j has a neighbor with color i. The Grundy chromatic number Γ(G), is the largest integer k for which there exists a Grundy k-coloring for G. In this note we first give an interpretation of Γ(G) in terms of the total graph of G, when G is the complement of a...
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Let G be a connected graph. Let f be a proper k -coloring of G and Π = (R_1, R_2, . . . , R_k) bean ordered partition of V (G) into color classes. For any vertex v of G, define the color code c_Π(v) of v with respect to Π to be a k -tuple (d(v, R_1), d(v, R_2), . . . , d(v, R_k)), where d(v, R_i) is the min{d(v, x)|x ∈ R_i}. If distinct vertices have distinct color codes, then we call f a locat...
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The Grundy number of a graph G is the maximum number k of colors used to color the vertices of G such that the coloring is proper and every vertex x colored with color i, 1 ≤ i ≤ k, is adjacent to (i− 1) vertices colored with each color j, 1 ≤ j ≤ i− 1. In this paper we give bounds for the Grundy number of some graphs and cartesian products of graphs. In particular, we determine an exact value ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.06.044