A note on the ultimate categorical matching in a graph (Q1849960)

Let \(m(G)\) denote the number of vertices covered by a maximum matching in a (simple undirected) graph \(G\). The ultimate categorical matching \(m^\ast (G):=\lim_{n\to\infty}m(G^n)^{1/n}\) where the categorical product \(\times\) is used. The author proves that \(m^\ast (G\times H)=m^\ast (G)\times m^\ast (H)\) for any graphs \(G\) and \(H\). This solves a question of \textit{M. H. Albert} et al. [Discrete Math. 232, 1-9 (2001; Zbl 0971.05090)].