English

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 kk-orthogonal colouring, then so does their tensor graph. This provides an upper bound on the kk-orthogonal chromatic number for general tensor graphs. Lastly, two other conditions for a tensor graph to have a perfect kk-orthogonal colouring are given.

Keywords

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

R2 v1 2026-06-23T18:51:32.334Z