Bujtas, C. and Sampathkumar, E. and Tuza, Z. and Pushpalatha, L. and Vasundhara, R. C.
(2011)
*Improper C-colorings of graphs.*
DISCRETE APPLIED MATHEMATICS, 159 (4).
pp. 174-186.
ISSN 0166-218X

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## Abstract

For an integer k >= 1, the k-improper upper chromatic number (chi) over bar (k-imp)(G) of a graph G is introduced here as the maximum number of colors permitted to color the vertices of G such that, for any vertex nu in G, at most k vertices in the neighborhood N(nu) of nu receive colors different from that of nu. The exact value of (chi) over bar (k-imp) is determined for several types of graphs, and general estimates are given in terms of various graph invariants, e.g. minimum and maximum degree, vertex covering number, domination number and neighborhood number. Along with bounds on (chi) over bar (k-imp) for Cartesian products of graphs, exact results are found for hypercubes. Also, the analogue of the Nordhaus-Gaddum theorem is proved. Moreover, the algorithmic complexity of determining (chi) over bar (k-imp) is studied, and structural correspondence between k-improper C-colorings and certain kinds of edge cuts is shown. (C) 2010 Elsevier B.V. All rights reserved.

Item Type: | Article |
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Uncontrolled Keywords: | Graph improper coloring; k-improper C-coloring; 3-consecutive coloring; Upper chromatic number; Edge cut |

Subjects: | E Mathematical Science > Mathematics |

Divisions: | Department of > Mathematics |

Depositing User: | Users 23 not found. |

Date Deposited: | 24 Jun 2019 09:24 |

Last Modified: | 24 Jun 2019 09:24 |

URI: | http://eprints.uni-mysore.ac.in/id/eprint/2558 |

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