Speaker: Daniel Johnston, Grand Valley State University

Title: On Rainbow Turán Numbers

Date: 04/10/2018

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

For a fixed graph F, we consider the maximum number of edges in a properly edge-colored graph on n vertices which does not contain a rainbow copy of F, that is, a copy of F all of whose edges receive a different color. This maximum, denoted by ex^*(n; F), is the rainbow Turán number of F, and its systematic study was initiated by Keevash, Mubayi, Sudakov and Verstr\"ate [Combinatorics, Probability and Computing 16 (2007)]. In this talk, we look ex^*(n; F) when F is a forest of stars, and consider bounds on ex^*(n; F) when F is a path with m edges, disproving a conjecture in the aforementioned paper for m = 4. This is based on joint work with Cory Palmer, Puck Rombach, and Amites Sarkar.