Total Colourings of Direct Product Graphs
Combinatorics
2020-08-06 v2
Abstract
A graph is k-total colourable if there is an assignment of k different colours to the vertices and edges of the graph such that no two adjacent nor incident elements receive the same colour. The total chromatic number of some direct product graphs are determined. In particular, a sufficient condition is given for direct products of bipartite graphs to have total chromatic number equal to its maximum degree plus one. Partial results towards the total chromatic number of the direct product of complete graphs are also established.
Cite
@article{arxiv.1807.05842,
title = {Total Colourings of Direct Product Graphs},
author = {Jeannette Janssen and Kyle MacKeigan},
journal= {arXiv preprint arXiv:1807.05842},
year = {2020}
}