Abstract
AbstractA 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 of its neighbours. We establish sufficient conditions for the existence of a perfect matching in K1,p-restricted graphs in terms of their connectivity and vertex degrees. These conditions imply, in particular, the classical Petersen’s result: any 2-edge-connected 3-regular graph contains a perfect matching.
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