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Detecting and Counting Small Pattern Graphs

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Author

Summary, in English

We study the induced subgraph isomorphism problem and the general subgraph isomorphism problem for small pattern graphs. We present a new general method for detecting induced subgraphs of a host graph isomorphic to a fixed pattern graph by reduction to polynomial testing for nonidentity with zero over a field of finite characteristic. It yields new upper time bounds for several pattern graphs on five vertices and provides an alternative combinatorial method for the majority of pattern graphs on four and three vertices. Since our method avoids the large overhead of fast matrix multiplication, it can be of practical interest even for larger pattern graphs. Next, we derive new upper time bounds on counting the number of isomorphisms between a fixed pattern graph with an independent set of size s and a subgraph of the host graph. We also consider a weighted version of the counting problem, when one counts the number of isomorphisms between the pattern graph and lightest subgraphs, providing a slightly slower combinatorial algorithm.

Publishing year

2015

Language

English

Pages

1322-1339

Publication/Series

SIAM Journal on Discrete Mathematics

Volume

29

Issue

3

Document type

Journal article

Publisher

Society for Industrial and Applied Mathematics

Topic

  • Discrete Mathematics

Keywords

  • subgraph and induced subgraph isomorphism
  • counting and detection of
  • subgraphs
  • polynomial testing
  • exact algorithms
  • randomized algorithms
  • rectangular matrix multiplication

Status

Published

ISBN/ISSN/Other

  • ISSN: 0895-4801