On the path partition number of 6-regular graphs
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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 n/d+1 paths. The conjecture has been proved for all d<6. We prove the conjecture for d=6.
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