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Long cycles in Hamiltonian graphs

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Abstract

We prove that if an n-vertex graph with minimum degree at least 3 contains a Hamiltonian cycle, then it contains another cycle of length n−o(n); in particular, this verifies, in an asymptotic form, a well-known conjecture due to Sheehan from 1975.

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Authors and Affiliations

  1. Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WB, UK

    António Girão

  2. Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok, 10330, Thailand

    Teeradej Kittipassorn

  3. Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, USA

    Bhargav Narayanan

Authors
  1. António Girão
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  2. Teeradej Kittipassorn
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  3. Bhargav Narayanan
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Correspondence to Bhargav Narayanan.

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Girão, A., Kittipassorn, T. & Narayanan, B. Long cycles in Hamiltonian graphs. Isr. J. Math. 229, 269–285 (2019). https://doi.org/10.1007/s11856-018-1798-6

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  • DOI: https://doi.org/10.1007/s11856-018-1798-6

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