Capacities of graphs and 2-matchings Original Research Article

A graph G is symmetric with respect to a functional FG(P) defined on the set of all the probability distributions on its vertex set if the distribution P∗ maximizing FG(P) is uniform on V(G). We show that the class of graphs which are symmetric for the functional appearing in the capacity formula of Cohen et al. (1968) and Gargano et al. (1993) coincides with the graphs admitting a 2-matching in the sense of Tutte (1947). This has an interesting implication for families of qualitatively independent partitions (in the sense of Rényi).