3Regular Maps on Closed Surfaces are Nearly Disti

Authors: Seiya Negami

Publish Date: 2015/09/10

Volume: 31, Issue: 6, Pages: 1929-1940

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Abstract

A kcoloring of a map MG on a closed surface with underlying graph G is said to be distinguishing if no automorphism of MG other than the identity map preserves the colors given by the coloring In particular if there is a distinguishing kcoloring of MG which uses color k at most once then MG is said to be nearly distinguishing k1colorable We shall show that any 3regular map on a closed surface is nearly distinguishing 3colorable unless it is one of the three exceptions

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