Hung-Hsun Hans Yu

On Colorful Kruskal--Katona Theorems

What is the maximum number of rainbow triangles in an edge-colored graph with $m$ edges and $r$ colors? Using entropic techniques, we prove an upper bound of $C_rm^{3/2}$ rainbow triangles with $C_r=\sqrt{\frac{2(r-2)}{9r}}$; this constant is best possible whenever there exists an affine plane of order $r-1$. We also s...