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Long cycles in hamiltonian graphs

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  • UserAntónio Girão (University of Cambridge)
  • ClockThursday 19 October 2017, 14:30-15:30
  • HouseMR12.

If you have a question about this talk, please contact Andrew Thomason.

In 1975, Sheehan conjectured that every d-regular hamiltonian graph contains a second hamiltonian cycle. This conjecture has been verified for all d greater than 22. In the light of Sheehan’s conjecture, it is natural to ask if regularity is genuinely necessary to force the existence of a second hamiltonian cycle, or if a minimum degree condition is enough. In this talk, we shall discuss a recent result which asserts that a hamiltonian graph with minimum degree 3 must contain another cycle of order at least n-o(n), thus answering, in an asymptotic form, the above question. This work is joint with Kittipassorn and Narayanan.

This talk is part of the Combinatorics Seminar series.

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