Read's conjecture explained

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]}

Notes and References

1. Baker . Matthew . January 2018 . Hodge theory in combinatorics . Bulletin of the American Mathematical Society . en . 55 . 1 . 57–80 . 10.1090/bull/1599 . 51813455 . 0273-0979. free . 1705.07960 .
2. R. C. Read, An introduction to chromatic polynomials, J. Combinatorial Theory 4 (1968), 52–71. MR0224505 (37:104)
3. Hoggar . S. G . 1974-06-01 . Chromatic polynomials and logarithmic concavity . Journal of Combinatorial Theory. Series B. en . 16 . 3 . 248–254 . 10.1016/0095-8956(74)90071-9 . free . 0095-8956.
4. Web site: Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial geometries. June. Huh.
5. 5 July 2022. He Dropped Out to Become a Poet. Now He's Won a Fields Medal.. 5 July 2022. Quanta Magazine. en.
6. Kalai . Gil . The Work of June Huh. Proceedings of the International Congress of Mathematicians 2022 . July 2022 . 1 - 16., pp. 2 - 4.
7. Huh . June . June Huh . Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs . 1008.4749 . Journal of the American Mathematical Society . 25 . 2012 . 907—927 . 10.1090/S0894-0347-2012-00731-0 . free.