The ultimate categorical matching in a graph Original Research Article

Let m(G) denote the number of vertices covered by a maximum matching in a graph G. We introduce m∗(G)=limn→∞m(Gn)1/n where the categorical graph product is used. We show that m∗(Ka,b)=2ab. Moreover, if G is bipartite, with parts A and B, has a matching which saturates A and A×B∪B×A has a perfect matching, then m∗G=2|A||B|.