Approximate path decompositions of regular graphs
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909216753582080 |
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| author | Montgomery, Richard Müyesser, Alp Pokrovskiy, Alexey Sudakov, Benny |
| author_facet | Montgomery, Richard Müyesser, Alp Pokrovskiy, Alexey Sudakov, Benny |
| contents | We show that the edges of any $d$-regular graph can be almost decomposed into paths of length roughly $d$, giving an approximate solution to a problem of Kotzig from 1957. Along the way, we show that almost all of the vertices of a $d$-regular graph can be partitioned into $n/(d+1)$ paths, asymptotically confirming a conjecture of Magnant and Martin from 2009. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02514 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximate path decompositions of regular graphs Montgomery, Richard Müyesser, Alp Pokrovskiy, Alexey Sudakov, Benny Combinatorics We show that the edges of any $d$-regular graph can be almost decomposed into paths of length roughly $d$, giving an approximate solution to a problem of Kotzig from 1957. Along the way, we show that almost all of the vertices of a $d$-regular graph can be partitioned into $n/(d+1)$ paths, asymptotically confirming a conjecture of Magnant and Martin from 2009. |
| title | Approximate path decompositions of regular graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2406.02514 |