 

Colloquia, Seminars, and Conferences
Colloquium
Monday, April 20^{th}, 2015 at 11 AM, NS 333
(Refreshments afterwards in room 334)
"Monochromatic cycle partitions"
Louis DeBiasio
Miami University
Abstract: Say that a graph G has property L if in every 2coloring of the edges, there exists a red cycle C_{1} and a blue cycle C_{2} having the property that C_{1} and C_{2} are vertex disjoint and the union of their vertex sets is equal to the vertex set of G (for simplicity, we allow for cycles on 1 and 2 vertices). Which graphs on n vertices have property L? Does there exist any graph on n vertices with property L? Lehel conjectured that for all n, the complete graph on n vertices has property L. Over the next 30 years there were many partial results ultimately leading to a proof by Bessy and Thomasse in 2009. In this talk, we will explore various strengthenings of Lehel's conjecture. That is, we will see some sufficient conditions and some necessary conditions for G to have property L. Along the way, we will discuss the regularityblowup method, the absorbing method, expanders, and (pseudo)random graphs. Based on joint work with Deepak Bal and Luke Nelsen. Seminars
The following research seminars meet weekly in the Natural Sciences Building. Everyone is welcome to attend. For more information, please contact corresponding coordinators.  
University of
Louisville, Department of Mathematics. Copyright 2006. All rights
reserved.
Comments to mailto:dwildstr@louisville.edu. 