Read's conjecture is a conjecture, first made by Ronald Read, about the

unimodality In mathematics, unimodality means possessing a unique mode. More generally, unimodality means there is only a single highest value, somehow defined, of some mathematical object. Unimodal probability distribution In statistics, a unimodal pr ...

of the coefficients of

chromatic polynomial The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a function of the number of colors and was originally defined by George David Birkhoff to study ...

s in the context of

graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

. 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. The Read–Hoggar conjecture had been unresolved for more than 40 years before

June Huh June Huh (full name: June E Huh, ; born 1983) is an Korean-American mathematician who is currently a professor at Princeton University. Previously, he was a professor at Stanford University. He was awarded the Fields Medal in 2022 and a MacAr ...

proved it in 2009, during his PhD studies, using methods from

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

., pp. 2–4.

References

Conjectures that have been proved Graph theory {{graph-stub