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.
The NP-completeness of automorphic colorings / Mazzuoccolo, Giuseppe. - In: DISCUSSIONES MATHEMATICAE. GRAPH THEORY. - ISSN 1234-3099. - STAMPA. - 30:4(2010), pp. 705-710. [10.7151/dmgt.1525]
The NP-completeness of automorphic colorings
MAZZUOCCOLO, Giuseppe
2010
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.
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