Linear arboricity of robust expanders
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909980379054080 |
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| author | Gao, Yuping Shan, Songling |
| author_facet | Gao, Yuping Shan, Songling |
| contents | In 1980, Akiyama, Exoo, and Harary conjectured that any graph $G$ can be decomposed into at most $\lceil(Δ(G)+1)/2\rceil$ linear forests. We confirm the conjecture for robust expanders of linear minimum degree.
As a consequence, the conjecture holds for dense quasirandom graphs of linear minimum degree
as well as for large $n$-vertex graphs with minimum degree arbitrarily close to $n/2$ from above. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Linear arboricity of robust expanders Gao, Yuping Shan, Songling Combinatorics In 1980, Akiyama, Exoo, and Harary conjectured that any graph $G$ can be decomposed into at most $\lceil(Δ(G)+1)/2\rceil$ linear forests. We confirm the conjecture for robust expanders of linear minimum degree. As a consequence, the conjecture holds for dense quasirandom graphs of linear minimum degree as well as for large $n$-vertex graphs with minimum degree arbitrarily close to $n/2$ from above. |
| title | Linear arboricity of robust expanders |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2405.18494 |