Abstract
In this paper we study the problem of finding a maximum induced d-degenerate subgraph in a given n-vertex graph from the point of view of exact algorithms. We show that for any fixed d one can find a maximum induced d-degenerate subgraph in randomized \((2-\varepsilon _d)^nn^{\mathcal{O}(1)}\) time, for some constant ε d > 0 depending only on d. Moreover, our algorithm can be used to sample inclusion-wise maximal induced d-degenerate subgraphs in such a manner that every such subgraph is output with probability at least (2 − ε d )− n; hence, we prove that their number is bounded by (2 − ε d )n.
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Pilipczuk, M., Pilipczuk, M. (2012). Finding a Maximum Induced Degenerate Subgraph Faster Than 2n . In: Thilikos, D.M., Woeginger, G.J. (eds) Parameterized and Exact Computation. IPEC 2012. Lecture Notes in Computer Science, vol 7535. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33293-7_3
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DOI: https://doi.org/10.1007/978-3-642-33293-7_3
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