DMS Combinatorics Seminar

Speaker: Isabel Harris

Title: General Results on \(k\)-Rainbow Avoiding Subgraphs

Abstract: A simple graph with \(e = E(G)\) avoids a \(k\)-rainbow coloring if any color appears on at least \(k+1\) edges of \(G\). For \(k ∈ P, ARk(G, n)\) is the maximum number of colors in an edge coloring of \(Kn\) so that in every copy of \(G\), some color occurs on at least \(k+1\) edges. \(G\) is \(ARk\)-bounded if \(ARk(G,n) ≤ c\) for some \(c ∈ P\) and all \(n\) sufficiently large.  In this talk we will discuss some results on finding \(ARk\)-bounded graphs for any \(k\).