Mathematics > Combinatorics
[Submitted on 4 Jun 2024
]
Title: Approximate path decompositions of regular graphs
Title: 正则图的近似路径分解
Abstract: 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.
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