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Finding a shortest cycle in a subspace of the cycle space of a graph

Author

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  • Chao, Fugang
  • Ren, Han
  • Cao, Ni

Abstract

Thomassen’s 3-path-condition shows that it is relatively easy for one to find a shortest cycle in a collection of cycles beyond a subspace of the cycle space of a connected graph and the real challenge is to find a shortest cycle contained in a given subspace of the cycle space of a graph. In this article we investigate the shorter cycle structures in a given subspace of a graph and find a set of cycles in a given graph containing much information about short cycles. We show that for a large range of subspaces of a graph satisfying a “parity condition”, there exists a polynomial time algorithm to find a shortest cycle in these subspaces. This makes a unified treatment of several famous algorithms. Finally we provide lower bounds of some types of short cycles in embedded graphs.

Suggested Citation

  • Chao, Fugang & Ren, Han & Cao, Ni, 2015. "Finding a shortest cycle in a subspace of the cycle space of a graph," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 393-398.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:393-398
    DOI: 10.1016/j.amc.2015.06.053
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