The challenges of unbounded treewidth in parameterised subgraph counting problems

Meeks, K. (2016) The challenges of unbounded treewidth in parameterised subgraph counting problems. Discrete Applied Mathematics, 198, pp. 170-194. (doi: 10.1016/j.dam.2015.06.019)

Abstract

Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised problems which involve finding or counting subgraphs with particular properties rely on bounding the treewidth of these subgraphs in some sense; here, we prove a number of hardness results for the situation in which this bounded treewidth condition does not hold, resulting in dichotomies for some special cases of the general subgraph counting problem. The paper also gives a thorough survey of known results on this subject and the methods used, as well as discussing the relationships both between multicolour and uncoloured versions of subgraph counting problems, and between exact counting, approximate counting and the corresponding decision problems.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Meeks, Dr Kitty
• Authors: Meeks, K.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Discrete Applied Mathematics
• Publisher: Elsevier
• ISSN: 0166-218X
• ISSN (Online): 1872-6771
• Copyright Holders: Copyright © 2015 The Authors
• First Published: First published in Discrete Applied Mathematics 2015 198:17-194
• Publisher Policy: Reproduced under a Creative Commons License