Balanced 1-Factorisations of 3- and 4-Regular Circulant Graphs

Jeremy Mitchell

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arXiv · 2411.19197

Balanced 1-Factorisations of 3- and 4-Regular Circulant Graphs

Jeremy Mitchell

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Abstract

We investigate 1-factorisations in which the 2-regular graphs that occur as the union of a pair of 1-factors appear an equal number of times across the unions of all pairs of 1-factors in the 1-factorisation. We call such 1-factorisations balanced 1-factorisations (B1Fs) and we present some results on B1Fs of 3- and 4-regular circulant graphs.

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Jeremy Mitchell. 2024-11-28. Balanced 1-Factorisations of 3- and 4-Regular Circulant Graphs. https://arxiv.org/abs/2411.19197

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