2 problems

Strengthened cycle-free chromatic discrepancy conjecture. For every integer $\ell\ge 3$, every $C_{\ell+1}$-free graph $G\ne K_{\ell}$ satisfies

Cycle-free chromatic discrepancy conjecture. For every integer $\ell\ge 2$, every $C_{\ell+1}$-free graph $G$ satisfies