Decomposing cubic graphs into isomorphic linear forests
Combinatorics
2025-07-09 v4
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 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.
Keywords
Cite
@article{arxiv.2210.11458,
title = {Decomposing cubic graphs into isomorphic linear forests},
author = {Gal Kronenberg and Shoham Letzter and Alexey Pokrovskiy and Liana Yepremyan},
journal= {arXiv preprint arXiv:2210.11458},
year = {2025}
}
Comments
49 pages, many figures