Fields institute,Room 210
Speaker: Daniel Soukup
Title: Monochromatic partitions of edge-colored infinite graphs
Abstract: Our goal is to find well behaved partitions of edge-colored infinite graphs following a long standing trend in finite combinatorics started by several authors including P. Erdős and R. Rado; in particular, we are interested in partitioning the vertices of complete or nearly complete graphs into monochromatic paths and powers of paths. One of our main results is that for every 2-edge-coloring of the complete graph on $\omega_1$ one can partition the vertices into two monochromatic paths of different colors. Our plan for the talk is to review some results from the literature (both on finite and infinite), sketch some of our results and the ideas involved and finally present the great deal of open problems we facing at the moment. This is a joint work with M. Elekes, L. Soukup and Z. Szentmiklóssy.