Orthogonal Colourings of Tensor Graphs
Combinatorics
2022-01-11 v2
Abstract
In this paper, perfect k-orthogonal colourings of tensor graphs are studied. First, the problem of determining if a given graph has a perfect 2-orthogonal colouring is reformulated as a tensor subgraph problem. Then, it is shown that if two graphs have a perfect -orthogonal colouring, then so does their tensor graph. This provides an upper bound on the -orthogonal chromatic number for general tensor graphs. Lastly, two other conditions for a tensor graph to have a perfect -orthogonal colouring are given.
Cite
@article{arxiv.2009.13576,
title = {Orthogonal Colourings of Tensor Graphs},
author = {Kyle MacKeigan},
journal= {arXiv preprint arXiv:2009.13576},
year = {2022}
}
Comments
8 pages, 2 figures