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Some Hard Families of Parameterized Counting Problems

Published:09 July 2015Publication History
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Abstract

We consider parameterized subgraph counting problems of the following form: given a graph G, how many k-tuples of its vertices induce a subgraph with a given property? A number of such problems are known to be #W[1]-complete; here, we substantially generalize some of these existing results by proving hardness for two large families of such problems. We demonstrate that it is #W[1]-hard to count the number of k-vertex subgraphs having any property where the number of distinct edge densities of labeled subgraphs that satisfy the property is o(k2). In the special case in which the property in question depends only on the number of edges in the subgraph, we give a strengthening of this result, which leads to our second family of hard problems.

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        cover image ACM Transactions on Computation Theory
        ACM Transactions on Computation Theory  Volume 7, Issue 3
        July 2015
        83 pages
        ISSN:1942-3454
        EISSN:1942-3462
        DOI:10.1145/2798085
        Issue’s Table of Contents

        Copyright © 2015 ACM

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 9 July 2015
        • Accepted: 1 September 2014
        • Revised: 1 June 2014
        • Received: 1 January 2014
        Published in toct Volume 7, Issue 3

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