Vertex coloring without large polychromatic stars

Bujtás, Csilla and Sampathkumar, E. and Tuza, Zsolt and Dominic, Charles and Pushpalatha, L. (2012) Vertex coloring without large polychromatic stars. Discrete Mathematics, 312 (14). 2102 - 2108. ISSN 1872-681X

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Given an integer k≥2, we consider vertex colorings of graphs in which no k-star subgraph Sk=K1,k is polychromatic. Equivalently, in a star-k-coloring the closed neighborhood Nv of each vertex v can have at most k different colors on its vertices. The maximum number of colors that can be used in a star-k-coloring of graph G is denoted by χ̄k⋆(G) and is termed the star-k upper chromatic number of G. We establish some lower and upper bounds on χ̄k⋆(G), and prove an analogue of the Nordhaus–Gaddum theorem. Moreover, a constant upper bound (depending only on k) can be given for χ̄k⋆(G), provided that the complement G¯ admits a star-k-coloring with more than k colors.

Item Type: Article
Additional Information: Special Issue: The Sixth Cracow Conference on Graph Theory, Zgorzelisko 2010
Uncontrolled Keywords: Graph coloring, Vertex coloring, Local condition, Upper chromatic number, C-coloring
Subjects: E Mathematical Science > Mathematics
Divisions: Department of > Mathematics
Depositing User: C Swapna Library Assistant
Date Deposited: 18 Jul 2019 09:42
Last Modified: 18 Jul 2019 09:42

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