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arXiv · 2210.11458

Decomposing cubic graphs into isomorphic linear forests

Gal Kronenberg·Shoham Letzter·Alexey Pokrovskiy·Liana Yepremyan
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Abstract

A common problem in graph colouring seeks to decompose the edge set of a given graph into few similar and simple subgraphs, under certain divisibility conditions. In 1987 Wormald conjectured that the edges of every cubic graph on $4n$ vertices can be partitioned into two isomorphic linear forests. We prove this conjecture for large connected cubic graphs. Our proof uses a wide range of probabilistic tools in conjunction with intricate structural analysis, and introduces a variety of local recolouring techniques.

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Gal Kronenberg, Shoham Letzter, Alexey Pokrovskiy, Liana Yepremyan. 2022-10-20. Decomposing cubic graphs into isomorphic linear forests. https://arxiv.org/abs/2210.11458

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