On the path partition number of 6‐regular graphs
Uriel Feige, Ella Fuchs · Journal of Graph Theory · 2022
Abstract Apath partition(also referred to as a linear forest) of a graph is a set of vertex‐disjoint paths which together contain all the vertices of . An isolated vertex is considered to be a path in this case. The path partition conjecture states that every ‐vertex ‐regular graph has a path partition with at most paths. The conjecture has been proved for all . We prove the conjecture for .