On maximum matchings in König–Egerváry graphs

For a graph GG let α(G),μ(G)α(G),μ(G), and τ(G)τ(G) denote its independence number, matching number, and vertex cover number, respectively. If α(G)+μ(G)=|V(G)|α(G)+μ(G)=|V(G)| or, equivalently, μ(G)=τ(G)μ(G)=τ(G), then GG is a König–Egerváry graph.In this paper we give a new characterization of König–Egerváry graphs.