Subgraph characterization of red/blue-split graph and kőnig egerváry graphs

Authors:
Ephraim Korach;Thành Nguyen;Britta Peis
Affiliations:
Ben-Gurion University of the Negev, Israel;Cornell University, Ithaca, NY;Zentrum Fúr Angewandte Informatik (ZAIK) Universitát zu Kóln, Germany
Venue:
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Year:
2006

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Abstract

Kőnig-Egerváry graphs (KEGs) are the graphs whose maximum size of a matching is equal to the minimum size of a vertex cover. We give an excluded subgraph characterization of KEGs. We show that KEGs are a special case of a more general class of graph: Red/Blue-split graphs, and give an excluded subgraph characterization of Red/Blue-split graphs. We show several consequences of this result including theorems of Deming-Sterboul, Lovász, and Földes-Hammer. A refined result of Schrijver on the integral solution of certain systems of linear inequalities is also given through the result on the weighted version of Red/Blue-split graphs.