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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## Abstract

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 |
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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 |

URI: | http://eprints.uni-mysore.ac.in/id/eprint/9361 |

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