Sen Cao

Albertson's Conjecture for Chromatic Numbers at Most 29

Albertson's conjecture asserts that every finite simple graph $G$ with $\chi(G) \ge r$ satisfies $\operatorname{cr}(G) \ge \operatorname{cr}(K_r)$. Building on Cranston's verification for $r \le 24$ and his reduction of $r \in \{25,26\}$ to three residual orders, we eliminate those residual cases and then prove the cas...