Forbidden subgraphs and the Kőnig property

Abstract A graph has the Kőnig property if its matching number equals its transversal number. Lovasz proved a characterization of graphs having the Kőnig property by forbidden subgraphs, restricted to graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovaszʼs result to a characterization of all graphs having the Kőnig property in terms of forbidden configurations (certain arrangements of a subgraph and a maximum matching). In this work, we prove a characterization of graphs having the Kőnig property in terms of forbidden subgraphs which is a strengthened version of the characterization by Korach et al. As a consequence of our characterization of graphs with the Kőnig property, we prove a forbidden subgraph characterization for the class of edge-perfect graphs.