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ISAAC
2007
Springer

The Complexity of Finding Subgraphs Whose Matching Number Equals the Vertex Cover Number

9 years 1 months ago
The Complexity of Finding Subgraphs Whose Matching Number Equals the Vertex Cover Number
The class of graphs where the size of a minimum vertex cover equals that of a maximum matching is known as K¨onig-Egerv´ary graphs. K¨onig-Egerv´ary graphs have been studied extensively from a graph theoretic point of view. In this paper, we introduce and study the algorithmic complexity of finding maximum K¨onig-Egerv´ary subgraphs of a given graph. More specifically, we look at the problem of finding a minimum number of vertices or edges to delete to make the resulting graph K¨onig-Egerv´ary. We show that both these versions are NP-complete and study their complexity from the points of view of approximation and parameterized complexity. En route, we point out an interesting connection between the vertex deletion version and the A G V C problem where one is interested in the parameterized complexity of the V C problem when parameterized by the ‘additional number of vertices’ needed...
Sounaka Mishra, Venkatesh Raman, Saket Saurabh, So
Added 08 Jun 2010
Updated 08 Jun 2010
Type Conference
Year 2007
Where ISAAC
Authors Sounaka Mishra, Venkatesh Raman, Saket Saurabh, Somnath Sikdar, C. R. Subramanian
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