Complexity of determining the irregular chromatic index of a graph [chapter]

Julien Bensmail
2013 The Seventh European Conference on Combinatorics, Graph Theory and Applications  
A graph G is locally irregular if adjacent vertices of G have different degrees. A k-edge colouring φ of G is locally irregular if each of the k colours of φ induces a locally irregular subgraph of G. The irregular chromatic index χ 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 χ irr (G) = 2 is NP-complete, even when G is assumed to be a planar graph with maximum degree at most 6.
doi:10.1007/978-88-7642-475-5_104 fatcat:3ankb7fbxnhlzgdvojnnzx7jaa