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 $k$.