DMS Combinatorics Seminar

Speaker: Isabel Harris (Auburn)

Title: Avoiding k-Rainbow Graphs in Edge Colorings of K_n and other Families of Graphs

Abstract: A simple graph, G, avoids a k-rainbow edge coloring if any color appears on at least k+1 edges of G. For any positive integer k, the k-Anti-Ramsey Number, AR_k(G, H), is the maximum number of colors in an edge coloring of the graph H on such that no k-rainbow edge colored copy of G is a subgraph of H. This talk will focus specifically on the edge colorings of complete graphs with n vertices, AR_k(G,K_n)=AR_k(G,n). We will say G is AR_k-bounded if AR_k(G,n) is bounded by some positive integer c for all n sufficiently large.  In this talk we will discuss which simple graphs are AR_k-bounded on the complete graph for any k. Additionally, we will explore some results for AR_k(G,H), where H is not the complete graph.