Casey Tompkins: The saturation number of rainbow colored graphs

We resolve a conjecture Barrus, Ferrara, Vandenbusshe and Wender about the saturation number of

rainbow colored graphs. Namely, we show that the saturation number of an $n$-vertex $t$-colored

graph forbidding a rainbow $K_k$ is $\Theta(n \log(n))$. More precise bounds are given in the case

of triangles. The proof involves a generalization of an old theorem of Katona and Szemeredi.

Several other results regarding colored saturated graphs will also be presented.

This project was carried out at the GRWC workshop jointly with M. Ferrara, D. Johnston, S. Loeb,

F. Pfender, A. Schulte, H. Smith, E. Sullivan, M. Tait.