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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## Abstract

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 |
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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 |

URI: | http://eprints.uni-mysore.ac.in/id/eprint/5348 |

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