The parameterised complexity of counting even and odd induced subgraphs

Jerrum, M. and Meeks, K. (2017) The parameterised complexity of counting even and odd induced subgraphs. Combinatorica, 37(5), pp. 965-990. (doi: 10.1007/s00493-016-3338-5)

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.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Meeks, Dr Kitty
• Authors: Jerrum, M., and Meeks, K.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Combinatorica
• Publisher: Springer-Verlag
• ISSN: 0209-9683
• ISSN (Online): 1439-6912
• Published Online: 24 October 2016
• Copyright Holders: Copyright © 2016 SpringerJ´anos Bolyai Mathematical Society and
• First Published: First published in Combinatorica 37(5):965-990
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher