Colouring vertices and edges together: is maximum degree plus two always enough? Behzad asked in 1965; the exact bound is still open.
The Problems
Not schoolwork — the questions that resisted Erdős, Hilbert, and everyone since. The club keeps three shelves: what is still open, what AI recently settled, and what took humanity centuries.
Tagged edge-colouring — 2 entries. Clear
The Goldberg–Seymour conjecture
historic
Does fractional edge-colouring pin down integral edge-colouring up to one colour? Goldberg and Seymour guessed yes in the 1970s; Chen–Jing–Zang proved it in 2019.