Packing paths of length at least two

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Abstract

We give a simple proof for Kaneko's theorem which gives a sufficient and necessary condition for the existence of vertex disjoint paths in a graph, each of length at least two, that altogether cover all vertices of the original graph. Moreover we generalize this theorem and give a formula for the maximum number of vertices that can be covered by such a path system.

Keywords

Path factor
Graph factor
Packing

Cited by (0)

1

Research supported by OTKA grant OTKA T 043520 and JSPS.

2

Research supported by OTKA grant OTKA T 029772, T 037547 and T 030059.