Orthogonal colourings of tensor graphs
DOI:
https://doi.org/10.55016/ojs/cdm.v20i2.74490Abstract
Perfect $k$-orthogonal colourings of tensor product graphs are studied in this article. 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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