# Many Hamiltonian Cycles

 COMPUTER SCIENCE/DISCRETE MATH I Topic: Many Hamiltonian Cycles Speaker: Jeff Kahn Affiliation: Rutgers University Date: Monday, May 1 Time/Room: 11:15am - 12:15pm/S-101

We'll begin with the following theorem, which proves a conjecture of S\'ark\"ozy, Selkow and Szemer\'edi, and try to use it as an excuse to talk about other things (perhaps including Br\'egman's Theorem, entropy, the incremental random method," statistical physics...). Theorem. Any n-vertex Dirac graph (i.e. graph of minimum degree at least $n/2$) contains at least $(2-o(1))^{-n}n!$ Hamiltonian cycles.