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On matching extendability of lexicographic products
A graph G of even order is â„“-extendable if it is of order at least 2â„“ + 2, contains a matching of size â„“, and if every such matching is contained in a perfect matching of G. In this paper, we study the extendability of lexicographic products of graphs. We characterize graphs G and H such that their lexicographic product is not 1-extendable. We also provide several conditions on the graphs G and H under which their lexicographic product is 2-extendable