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Conference Paper

A Quartic Kernel for Pathwidth-One Vertex Deletion

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Philip, G., Raman, V., & Villanger, Y. (2010). A Quartic Kernel for Pathwidth-One Vertex Deletion. In D. M. Thilikos (Ed.), Graph Theoretic Concepts in Computer Science (pp. 196-207). Berlin: Springer. doi:10.1007/978-3-642-16926-7_19.

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The pathwidth of a graph is a measure of how path-like the graph is. Given a graph G and an integer k, the problem of finding whether there exist at most k vertices in G whose deletion results in a graph of pathwidth at most one is \npc{}. We initiate the study of the parameterized complexity of this problem, parameterized by k. We show that the problem has a quartic vertex-kernel: We show that, given an input instance (G=(V,E),k);|V|=n, we can construct, in polynomial time, an instance (G',k') such that (i) (G,k) is a YES instance if and only if (G',k') is a YES instance, (ii) G' has \Oh(k^4}) vertices, and (iii) k'≤ k. We also give a fixed parameter tractable (FPT) algorithm for the problem that runs in \Oh(7^{kk⋅ n²) time.