Abstract
In the k-Path problem we are given an n-vertex graph G together with an integer k and asked whether G contains a path of length k as a subgraph. We give the first subexponential time, polynomial space parameterized algorithm for k-Path on planar graphs, and more generally, on H-minor-free graphs. The running time of our algorithm is \(O(2^{O(\sqrt{k}\log^2 k)}n^{O(1)})\).
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Lokshtanov, D., Mnich, M., Saurabh, S. (2011). Planar k-Path in Subexponential Time and Polynomial Space. In: Kolman, P., KratochvÃl, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 2011. Lecture Notes in Computer Science, vol 6986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25870-1_24
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DOI: https://doi.org/10.1007/978-3-642-25870-1_24
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