Speaker: Uri Rabinovich (U. Haifa)
Title: SOME EXTREMAL PROBLEMS ABOUT SIMPLICIAL COMPLEXES
Abstract:
We shall discuss the following three issues:
* The existence of Hamiltonian d-cycles, i.e., simple d-cycles containing a spanning d-hypertree of a complete d-complex K_n^d;
* The existence of a distribution D over spanning d-hypertrees T of K_n^d, so that for ANY
(d-1)-cycle C there, the expected size of the d-filling of C with respect to a random T from D is Omega(n^d);
* The existence of f(k,d) such that any d-simplex of rank r with > f(k,d)*r d-faces contains
a simple d-cycle of size k or more.
Based on joint works with Ilan Newman and Roy Meshulam.