Colloquium: Michael Young (Iowa State)

Event Details

Title: The anti-Ramsey number of a matching.

Abstract: In classical Ramsey theory a finite set of objects are colored (or partitioned), and we determine how many objects are necessary to guarantee that at least one of the color classes contains some given structure. Anti-Ramsey theory is the study of determining how many colors are necessary to guarantee that the given structure occurs across the color classes.

An edge coloring of a graph G is called rainbow if every edge of G has a distinct color. The anti-Ramsey number, ar(H, G) is the minimum number of colors necessary to guarantee that any coloring of H will contain a rainbow copy of G.  A matching of graph is a set of pairwise disjoint edges. In this talk, we discuss known results about the anti-Ramsey numbers where G is a matching in a graph or hypergraph and their relationship with Turán numbers.