Hajós conjectured every graph with no K_n+1-subdivision is n-colorable. The conjecture is true for n ≤ 3. However, Catlin disproved the conjecture for n ≥ 6. It remains open for n = 4 and 5. In this talk, I will introduce the motivation and background of the chromatic number problem on graphs with no K₅-subdivision. I will propose the plan of my future works regarding this problem. Some of my previous works related to the problem will also be mentioned.

海报