The irregular chromatic index of trees

Olivier Baudon (1) , Julien Bensmail (1) , Eric Sopena (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

A graph G is locally irregular if adjacent vertices of G have distinct degrees. An edge colouring of G is locally irregular if each of its colours induces a locally irregular subgraph of G. The irregular chromatic index of G refers to the least number of colours used by a locally irregular edge colouring of G (if any). We propose a linear-time algorithm for determining the irregular chromatic index of any tree.

Mots clés: locally irregular edge colouring; irregular chromatic index; tree; algorithm

Domaines: Mathématique discrète [cs.DM]

Olivier Baudon, Julien Bensmail, Eric Sopena. The irregular chromatic index of trees. 2013. ⟨hal-00805122⟩