Discussiones Mathematicae Graph Theory 30(4) (2010) 705-710
doi: 10.7151/dmgt.1525

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THE NP-COMPLETENESS OF AUTOMORPHIC COLORINGS

Giuseppe Mazzuoccolo

Dipartimento di Matematica
Università di Modena e Reggio Emilia
via Campi 213/B, 41125 Modena, Italy

Abstract

Given a graph G, an automorphic edge(vertex)-coloring of G is a proper edge(vertex)-coloring such that each automorphism of the graph preserves the coloring. The automorphic chromatic index (number) is the least integer k for which G admits an automorphic edge(vertex)-coloring with k colors. We show that it is NP-complete to determine the automorphic chromatic index and the automorphic chromatic number of an arbitrary graph.

Keywords: NP-complete problems, chromatic parameters, graph coloring, computational complexity.

2010 Mathematics Subject Classification: 68Q17, 05C15.

References

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Received 30 November 2009
Revised 8 February 2010
Accepted 11 February 2010