Colloquium

Thursday, Oct. 18, 2007

4:00 PM, BAC 219

Speaker: Felix Lazebnik, University of Delaware, Newark, Delaware

Host: Tao Jiang

Title: On Graphs Defined by Some Systems of Equations

Abstract:

In this talk I will present a simple method for constructing
infinite families of graphs defined by a class of systems of
equations over commutative rings.  The graphs in all such families
possess properties including regularity or bi-regularity, existence
of special vertex colorings, and existence of covering maps between
every two members of the same family (hence, embedded spectra).
Another general property is that nearly every graph constructed in
this manner edge-decomposes either the complete, or complete
bipartite, graph which it spans.

In many instances, specializations of these constructions have
proved useful in various graph theory problems, but especially in
many extremal problems which deal with cycles in graphs. I will
explain motivations for these constructions, survey both old and
new related results, applications, and state some open questions.