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 ...

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 stu ...

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 conn ...

. In 1974,

S. G. Hoggar S is the nineteenth letter of the English alphabet. S may also refer to: History * an Anglo-Saxon charter's number in Peter Sawyer's, catalogue Language and linguistics * Long s (ſ), a form of the lower-case letter s formerly used where " ...

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., pp. 2–4.

References

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