Read's conjecture

Read's conjecture is a conjecture, first made by Ronald Read, about the unimodality of the coefficients of chromatic polynomials in the context of graph theory.^[1][2] In 1974, S. G. Hoggar tightened this to the conjecture that the coefficients must be strongly log-concave. Hoggar's version of the conjecture is called the Read–Hoggar conjecture.^[3][4]

The Read–Hoggar conjecture had been unresolved for more than 40 years before June Huh proved it in 2009, during his PhD studies, using methods from algebraic geometry.^[1][5][6][7]