Complexity of determining the irregular chromatic index of a graph

Julien Bensmail (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

A graph G is locally irregular if adjacent vertices of G have different degrees. A k-edge colouring phi of G is locally irregular if each of the k colours of phi induces a locally irregular subgraph of G. The irregular chromatic index chi_{irr}'(G) of G is the least number of colours used by a locally irregular edge colouring of G (if any). We show that determining whether chi_{irr}'(G)=2 is NP-complete, even when G is assumed to be a planar graph with maximum degree at most 6.

Domaines: Mathématique discrète [cs.DM]

Julien Bensmail. Complexity of determining the irregular chromatic index of a graph. 2013. ⟨hal-00789172v2⟩