Abstract :
R. Ahlswede and N. Cai [Information and control: matching channels, IEEE Trans. Inform. Theory 44 (2) (1998) 542–563] studied the asymptotic behavior of matching numbers ν(G⊗n)ν(G⊗n) for the nn-th powers of a bipartite graph GG and proved the existence of the matching capacity γ(G)=limn→∞1nlogν(G⊗n). Moreover, they proved that γ(G)=maxmin(P,Q)∈K(G){H(P),H(Q)}γ(G)=maxmin(P,Q)∈K(G){H(P),H(Q)}, where HH is the entropy function and K(G)K(G) is the set of König–Hall pairs of distributions defined in Section 2. In this paper an iterative method of computing the matching capacity of a bipartite graph GG in which each vertex of degree ≥2 is adjacent to at least one vertex of degree 1 is presented and its exponentially fast convergence is shown.
