König Deletion Sets and Vertex Covers above the Matching Size

Authors:
Sounaka Mishra;Venkatesh Raman;Saket Saurabh;Somnath Sikdar
Affiliations:
Indian Institute of Technology, Chennai, India 600 036;The Institute of Mathematical Sciences, Chennai, India 600 113;The University of Bergen, Norway;The Institute of Mathematical Sciences, Chennai, India 600 113
Venue:
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Year:
2008

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Abstract

A graph is König-Egerváry if the size of a minimumvertex cover equals the size of a maximum matching in the graph. Weshow that the problem of deleting at most k vertices tomake a given graph König-Egerváry is fixed-parametertractable with respect to k. This is proved usinginteresting structural theorems on matchings and vertex coverswhich could be useful in other contexts.We also show an interesting parameter-preserving reduction fromthe vertex-deletion version of red/blue-split graphs [4,9] to aversion of Vertex Cover and as a by-product obtain1 the best-known exact algorithm for the optimization versionof Odd Cycle Transversal [15];1 fixed-parameter algorithms for several vertex-deletionproblems including the following: deleting k vertices tomake a given graph (a) bipartite [17], (b) split [5], and (c)red/blue-split [7].