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arXiv · 2009.13576

Orthogonal Colourings of Tensor Graphs

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

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Kyle MacKeigan. 2022-01-10. Orthogonal Colourings of Tensor Graphs. https://arxiv.org/abs/2009.13576

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