# Improper C-colorings of graphs

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

## Abstract

For an integer k≥1, the k-improper upper chromatic number χ̄k-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 ν in G, at most k vertices in the neighborhood N(ν) of ν receive colors different from that of ν. The exact value of χ̄k-impis 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 χ̄k-imp for Cartesian products of graphs, exact results are found for hypercubes. Also, the analogue of the NordhausGaddum theorem is proved. Moreover, the algorithmic complexity of determining χ̄ k-imp is studied, and structural correspondence between k-improper C-colorings and certain kinds of edge cuts is shown. © 2010 Elsevier B.V. All rights reserved.

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

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Depositing User: | EPrints Admin |

Date Deposited: | 12 Dec 2012 08:40 |

Last Modified: | 05 Feb 2014 15:47 |

URI: | https://eprints.sztaki.hu/id/eprint/6591 |

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