On the complexity of determining the irregular chromatic index of a graph
Résumé
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 $\chi_{irr}'(G)$ of $G$ is the least number of colours used by a locally irregular edge-colouring of $G$ (if any). We show that the problem of determining the irregular chromatic index of a graph can be handled in linear time when restricted to trees, but it remains NP-complete in general.
Domaines
Mathématique discrète [cs.DM]
Origine : Fichiers produits par l'(les) auteur(s)
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