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* Princeton Discrete Math Seminar *
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Speaker: Lior Gishboliner (ETH Zurich)
Thursday September 30, 3:00 online.
Title: Cycles of many lengths in Hamiltonian graphs
Abstract:
In 1999, Jacobson and Lehel conjectured that for $k \geq 3$, every $k$-regular
Hamiltonian graph has cycles of at least linearly many different lengths.
This was further strengthened by Verstra\"{e}te, who asked whether
the regularity can be replaced with the weaker condition that the minimum
degree is at least 3. Despite attention from various researchers, until now the
best partial result towards both of these conjectures was a sqrt(n) lower bound
on the number of cycle lengths. We resolve these conjectures asymptotically, by
showing that the number of cycle lengths is at least n^{1-o(1)}.
Joint work with Bucic and Sudakov.
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Next week: Rajko Nenadov
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