A graph is called K1,p-restricted (p ≥ 3) if for every vertex of the graph there are at least p - 2 edges between any p neighbours of the vertex. In this article, new sufficient conditions for existence of a perfect matching in K1,p-restricted graphs are established. In particular, J. Petersen’s classical result that every 2-edge connected 3-regular graph contains a perfect matching follows from these conditions.
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