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  • Björklund, Andreas, et al. (author)
  • Counting Closed Trails
  • 2013
  • In: Information Processing Letters. - : Elsevier BV. - 0020-0190. ; 113:1-2, s. 1-3
  • Journal article (peer-reviewed)abstract
    • 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.
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Type of publication
journal article (1)
Type of content
peer-reviewed (1)
Author/Editor
Kaski, Petteri (1)
Björklund, Andreas (1)
University
Lund University (1)
Language
English (1)
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Natural sciences (1)
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