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Counting Closed Trails

På svenska

Author

  • Andreas Björklund
  • Petteri Kaski

Summary, in English

A closed trail is a connected graph whose every vertex is incident to an even number of edges. We give a deterministic algorithm that in time $2^{m/2}poly(m,n)$ finds the number of closed trails in a given graph G with n vertices and m edges. Moreover, within the same time bound we can determine every possible vertex set of a closed trail in G, together with the associated number of closed trails. Our algorithm can be used to deterministically find the longest cycle in an n-vertex claw-free graph in time $2^{n/2}poly(m,n)$ via a framework presented by Broersma et al. (in press, http://dx.doi.org/10.1007/s00453-011-9576-4) [5], thus improving both upon the $O(1.66^n)$ time randomized algorithm for general graphs (Björklund, 2010, http://dx.doi.org/10.1109/FOCS.2010.24, [1]), as well as the $O(1.69^n)$ time deterministic algorithm for claw-free graphs by Broersma et al.

Publishing year

2013

Language

English

Pages

1-3

Publication/Series

Information Processing Letters

Volume

113

Issue

1-2

Document type

Journal article (letter)

Publisher

Elsevier

Topic

  • Computer Science

Status

Published

Project

  • Exact algorithms

Research group

  • Algorithms

ISBN/ISSN/Other

  • ISSN: 0020-0190