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Combinatorica

, Volume 37, Issue 5, pp 965–990 | Cite as

The parameterised complexity of counting even and odd induced subgraphs

  • Mark Jerrum
  • Kitty MeeksEmail author
Original Paper

Abstract

We consider the problem of counting, in a given graph, the number of induced k-vertex subgraphs which have an even number of edges, and also the complementary problem of counting the k-vertex induced subgraphs having an odd number of edges. We demonstrate that both problems are #W[1]-hard when parameterised by k, in fact proving a somewhat stronger result about counting subgraphs with a property that only holds for some subset of k-vertex subgraphs which have an even (respectively odd) number of edges. On the other hand, we show that each of the problems admits an FPTRAS. These approximation schemes are based on a surprising structural result, which exploits ideas from Ramsey theory.

Mathematics Subject Classification (2000)

68Q25 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Mathematical SciencesQueen Mary University of LondonLondonUK
  2. 2.School of Computing ScienceUniversity of GlasgowGlasgowUK

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