Vertex coloring without large polychromatic stars

Csilla Bujtas, and Sampathkumar, E. and Zsolt Tuza, and Charles Dominic, and Pushpalatha, L. (2012) Vertex coloring without large polychromatic stars. DISCRETE MATHEMATICS, 312 (14, SI). pp. 2102-2108.

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Given an integer k >= 2, we consider vertex colorings of graphs in which no k-star subgraph S-k = K-1,K-k is polychromatic. Equivalently, in a star-k]-coloring the closed neighborhood NI v I of each vertex nu 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 k.(G) and is termed the star-k] upper chromatic number of G. We establish some lower and upper bounds on (chi) over bar (k*) (G), and prove an analogue of the Nordhaus-Gaddum theorem. Moreover, a constant upper bound (depending only on k) can be given for (chi) over bar (k*) (G), provided that the complement (G) over bar admits a star-k]-coloring with more than k colors. (C) 2011 Elsevier B.V. All rights reserved.

Item Type: Article
Uncontrolled Keywords: Graph coloring; Vertex coloring; Local condition; Upper chromatic number; C-coloring
Subjects: Physical Sciences > Mathematics
Divisions: PG Campuses > Manasagangotri, Mysore > Mathematics
Depositing User: Swamy D
Date Deposited: 15 May 2013 13:54
Last Modified: 24 Aug 2013 09:17

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