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arXiv · 1911.08397

On the path partition number of 6-regular graphs

Uriel Feige·Ella Fuchs
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Abstract

A path partition (also referred to as a linear forest) of a graph $G$ is a set of vertex-disjoint paths which together contain all the vertices of $G$. An isolated vertex is considered to be a path in this case. The path partition conjecture states that every $n$-vertices $d$-regular graph has a path partition with at most $\frac{n}{d+1}$ paths. The conjecture has been proved for all $d<6$. We prove the conjecture for $d=6$.

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Uriel Feige, Ella Fuchs. 2019-11-19. On the path partition number of 6-regular graphs. https://arxiv.org/abs/1911.08397

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