Abstract:
A graph
G of even order is
ℓ-extendable if it is of order at least 2
ℓ + 2, contains a matching of size
ℓ, 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.