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arXiv · 2402.18457

Perfect colourings of simplices and hypercubes in dimension four and five with few colours

Dirk Frettlöh
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Abstract

A vertex colouring of some graph is called perfect if each vertex of colour $i$ has the same number $a_{ij}$ of neighbours of colour $j$. Here we determine all perfect colourings of the edge graphs of the hypercube in dimensions 4 and 5 by two and three colours, respectively. For comparison we list all perfect colourings of the edge graphs of the simplex in dimensions 4 and 5, respectively.

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Dirk Frettlöh. 2024-02-28. Perfect colourings of simplices and hypercubes in dimension four and five with few colours. https://arxiv.org/abs/2402.18457

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