
A graph is called König-Egerváry if the size of a minimum vertex cover equals that of a maximum matching in the graph. These graphs have been extensively studied from a graph-theoretic point of view. The authors introduce and study the algorithmic complexity of finding König-Egerváry subgraphs of a given graph. They show that different problems in this context are NP-complete.
unique game conjecture, Analysis of algorithms and problem complexity, vertex cover, König vertex/edge deletion sets, maximum matching, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), König graphs, Graph algorithms (graph-theoretic aspects), above guarantee vertex cover, approximation algorithms, parameterized complexity
unique game conjecture, Analysis of algorithms and problem complexity, vertex cover, König vertex/edge deletion sets, maximum matching, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), König graphs, Graph algorithms (graph-theoretic aspects), above guarantee vertex cover, approximation algorithms, parameterized complexity
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