Decomposing cubic graphs into isomorphic linear forests
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909677749534720 |
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| author | Kronenberg, Gal Letzter, Shoham Pokrovskiy, Alexey Yepremyan, Liana |
| author_facet | Kronenberg, Gal Letzter, Shoham Pokrovskiy, Alexey Yepremyan, Liana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_11458 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Decomposing cubic graphs into isomorphic linear forests Kronenberg, Gal Letzter, Shoham Pokrovskiy, Alexey Yepremyan, Liana Combinatorics 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. |
| title | Decomposing cubic graphs into isomorphic linear forests |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2210.11458 |