Kalai–Meshulam chromatic conjecture on induced cycles

Let $G$ be a graph, and let the chromatic number of $G$ be its minimum number of colors in a proper vertex coloring. An induced cycle is a cycle whose vertices induce exactly the edges of the cycle.

Kalai–Meshulam chromatic conjecture. A graph with high enough chromatic number has an induced cycle of length divisible by three.

This conjecture was proved by Bonamy, Charbit, and Thomassé, and later generalized by Scott and Seymour.