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]
Referencesedit
^ abBaker, Matthew (January 2018). "Hodge theory in combinatorics". Bulletin of the American Mathematical Society. 55 (1): 57–80. arXiv:1705.07960. doi:10.1090/bull/1599. ISSN 0273-0979. S2CID 51813455.
^R. C. Read, An introduction to chromatic polynomials, J. Combinatorial Theory 4 (1968), 52–71. MR0224505 (37:104)
^Hoggar, S. G (1974-06-01). "Chromatic polynomials and logarithmic concavity". Journal of Combinatorial Theory. Series B. 16 (3): 248–254. doi:10.1016/0095-8956(74)90071-9. ISSN 0095-8956.
^Huh, June. "Hard Lefschetz theorem and Hodge-Riemann relations for combinatorial geometries" (PDF).
^"He Dropped Out to Become a Poet. Now He's Won a Fields Medal". Quanta Magazine. 5 July 2022. Retrieved 5 July 2022.
^Kalai, Gil (July 2022). "The Work of June Huh" (PDF). Proceedings of the International Congress of Mathematicians 2022: 1–16., pp. 2–4.
^Huh, June (2012). "Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs". Journal of the American Mathematical Society. 25: 907–927. arXiv:1008.4749. doi:10.1090/S0894-0347-2012-00731-0.
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read, conjecture, conjecture, first, made, ronald, read, about, unimodality, coefficients, chromatic, polynomials, context, graph, theory, 1974, hoggar, tightened, this, conjecture, that, coefficients, must, strongly, concave, hoggar, version, conjecture, call. 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 References edit a b Baker Matthew January 2018 Hodge theory in combinatorics Bulletin of the American Mathematical Society 55 1 57 80 arXiv 1705 07960 doi 10 1090 bull 1599 ISSN 0273 0979 S2CID 51813455 R C Read An introduction to chromatic polynomials J Combinatorial Theory 4 1968 52 71 MR0224505 37 104 Hoggar S G 1974 06 01 Chromatic polynomials and logarithmic concavity Journal of Combinatorial Theory Series B 16 3 248 254 doi 10 1016 0095 8956 74 90071 9 ISSN 0095 8956 Huh June Hard Lefschetz theorem and Hodge Riemann relations for combinatorial geometries PDF He Dropped Out to Become a Poet Now He s Won a Fields Medal Quanta Magazine 5 July 2022 Retrieved 5 July 2022 Kalai Gil July 2022 The Work of June Huh PDF Proceedings of the International Congress of Mathematicians 2022 1 16 pp 2 4 Huh June 2012 Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs Journal of the American Mathematical Society 25 907 927 arXiv 1008 4749 doi 10 1090 S0894 0347 2012 00731 0 nbsp This graph theory related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Read 27s conjecture amp oldid 1193298118, wikipedia, wiki, book, books, library,
