Mathematical Structures Underlying Greedy Algorithms
FCT '81 Proceedings of the 1981 International FCT-Conference on Fundamentals of Computation Theory
Subgraph characterization of red/blue-split graph and kőnig egerváry graphs
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Triangle-free graphs with uniquely restricted maximum matchings and their corresponding greedoids
Discrete Applied Mathematics
König–Egerváry Graphs are Non-Edmonds
Graphs and Combinatorics
The critical independence number and an independence decomposition
European Journal of Combinatorics
Critical Independent Sets and König–Egerváry Graphs
Graphs and Combinatorics
Note: On maximum matchings in König-Egerváry graphs
Discrete Applied Mathematics
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The matching number of a graph is the maximum size of a set of vertex-disjoint edges. The transversal number is the minimum number of vertices needed to meet every edge. A graph has the Konig-Egervary property if its matching number equals its transversal number. Lovasz proved a characterization of graphs having the Konig-Egervary property by means of forbidden subgraphs within graphs with a perfect matching. Korach, Nguyen, and Peis proposed an extension of Lovasz's result to a characterization of all graphs having the Konig-Egervary property in terms of forbidden configurations (which are certain arrangements of a subgraph and a maximum matching). In this work, we prove a characterization of graphs having the Konig-Egervary property by means of forbidden subgraphs which is a strengthened version of the characterization by Korach et al. Using our characterization of graphs with the Konig-Egervary property, we also prove a forbidden subgraph characterization for the class of edge-perfect graphs.