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
2010-01-01

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.
NP-complete problems, chromatic parameters, graph coloring, computational complexity
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/927859
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 2
  • ???jsp.display-item.citation.isi??? ND
social impact