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SUMMARY:Long cycles in hamiltonian graphs - António Girão (University of
  Cambridge)
DTSTART:20171019T133000Z
DTEND:20171019T143000Z
UID:TALK85361@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:In 1975\, Sheehan conjectured that every d-regular hamiltonian
  graph contains a second hamiltonian cycle. This conjecture has been verif
 ied for all d greater than 22. In the light of Sheehan's conjecture\, it i
 s natural to ask if regularity is genuinely necessary to force the existen
 ce of a second hamiltonian cycle\, or if a minimum\ndegree condition is en
 ough. In this talk\, we shall discuss a recent result which asserts that a
  hamiltonian graph with minimum degree 3 must contain another cycle of ord
 er at least n-o(n)\, thus answering\, in an asymptotic form\, the above qu
 estion.\nThis work is joint with Kittipassorn and Narayanan.\n
LOCATION:MR12
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