Colloquium Abstracts

Date/Time/Location: Thursday Nov 2, 2017 from 3:00-3:50pm in BAC 219

Speaker/Affiliation: Gábor Sárközy, Worcester Polytechnic Institute and Alfréd Rényi Institute of Mathematics

Title: Monochromatic covers in edge-colored graphs and hypergraphs


We survey some results on the following problem:  Say we are given fixed positive integers s, t and a family of graphs F.  Minimizing over all t-edge colorings of the complete graph on n vertices, we ask for the maximum number of vertices that can be covered by at most s monochromatic members of F.  This problem unites two classical problems: at one end of the spectrum (s = 1) we have the Ramsey problem, while at the other end we have cover problems.  But there are some interesting problems "in-between" as well.
Several of the results are joint with András Gyárfás and/or Endre Szemerédi