On the complexity of determining the irregular chromatic index of a graph

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

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

An undirected simple graph G is locally irregular if adjacent vertices of G have different degrees. An edge-colouring phi of G is locally irregular if each colour class of phi induces a locally irregular subgraph of G. The irregular chromatic index of G is the least number of colours used by a locally irregular edge-colouring of G (if any). We show that the problem of determining the irregular chromatic index of a graph can be handled in linear time when restricted to trees, but remains NP-complete in general.

Domaines: Mathématique discrète [cs.DM]

Olivier Baudon, Julien Bensmail, Eric Sopena. On the complexity of determining the irregular chromatic index of a graph. 2013. ⟨hal-00921849v1⟩