Abstract
Let d and k be two given integers, and let G be a graph. Can we reduce the independence number of G by at least d via at most k graph operations from some fixed set S? This problem belongs to a class of so-called blocker problems. It is known to be co-NP-hard even if S consists of either an edge contraction or a vertex deletion. We further investigate its computational complexity under these two settings: we give a sufficient condition on a graph class for the vertex deletion variant to be co-NP-hard even if \(d=k=1\); in addition we prove that the vertex deletion variant is co-NP-hard for triangle-free graphs even if \(d=k=1\); we prove that the edge contraction variant is NP-hard for bipartite graphs but linear-time solvable for trees.
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