Approximate path decompositions of regular graphs
| Autor: | Montgomery, Richard, Müyesser, Alp, Pokrovskiy, Alexey, Sudakov, Benny |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 34 pages, 1 figure |
| Databáze: | arXiv |
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