# Combinatorics Seminar

When: Sunday, May 11, 10am

Where: Schreiber 309

Speaker: Ilan Newman, U. of Haifa

Title:
The combinatorics of simplicial complexes as a high dimensional
analog of Graphs

## Abstract:

We study simplicial complexes (here will mainly focus on 3-hypergraphs or
2-dim complexes) as a higher dimensional analogue of graph theory. Trees,
cycles and cuts are defined using basic linear algebra (via the matroid
approach, or basic algebraic topology), and several notions in relation
to the above objects are studied. Several features seem to go along the
corresponding theory for graphs, but some deviate considerably.

In particular, we show that there are trees with non-exposed edges
(trees with no leaves). We show that there are 2-dim Hamiltonian cycles
(for higher dimensions the problem is not yet settled), and have some
results on the size of the largest cuts. Other interesting results are
the extension of Balinski's Theorem (on the connectivity of the skeleton
of certain complexes).

The talk will be essentially a survey of the results and open problems
in the area. Only basic knowledge of combinatorics is assumed.

The talk is based on a joint work with Uri Rabinovich.

redesigned by barak soreq