Graph Theory and Combinatorics Seminar
- Event Type
- Seminar/Symposium
- Sponsor
- Department of Mathematics
- Location
- Altgeld Hall 147
- Date
- Dec 2, 2025 1:00 - 2:00 pm
- Speaker
- Ramon Garcia
- Contact
- Abhishek Dhawan
- adhawan2@illinois.edu
- Originating Calendar
- Combinatorics Research Area Calendar
Speaker: Ramon Garcia (UIUC)
Title. Density of rainbow triangles and properly colored $K_4$’s
Abstract. T.-W. Chao and H.-H. H. Yu showed in 2023 that a graph with $R$ red, $G$ green, and $B$ blue edges has at most $(2RGB)^{1/2}$ rainbow triangles. They proved this bound using entropy.
In this talk, I will present a fully computer-free flag-algebra proof of their result, along with a translation of the argument into a classical counting proof. The ideas in our proof lead to an even shorter entropy proof.
In addition, I will discuss a similar result that gives a sharp upper bound on the number of properly $3$-edge-colored $K_4$'s in graphs with $R$ red, $G$ green and $B$ blue edges.
Joint work with J\’ozsef Balogh, Peter Bradshaw and Bernard Lidick\'{y}.