Falsifiable on the site (label FALSIFIABLE; page last edited 6 December 2025). No result settles or claims to settle the question, so the problem is open; four published partial results are accepted partial claims, each on its refereed publication, Brown and Jung's case $a=b=3$, Balogh, Kostochka, Prince and Stiebitz's quasi-line and independence-number-2 cases, Song's graphs with no short hole and Longbrake and Tariq's pairs with a clique, and Song's even-hole-free case is a claimed partial claim, Song 2026.