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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs
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by June Huh PDF
J. Amer. Math. Soc. 25 (2012), 907-927 Request permission


The chromatic polynomial $\chi _G(q)$ of a graph $G$ counts the number of proper colorings of $G$. We give an affirmative answer to the conjecture of Read and Rota-Heron-Welsh that the absolute values of the coefficients of the chromatic polynomial form a log-concave sequence. The proof is obtained by identifying $\chi _G(q)$ with a sequence of numerical invariants of a projective hypersurface analogous to the Milnor number of a local analytic hypersurface. As a by-product of our approach, we obtain an analogue of Kouchnirenko’s theorem relating the Milnor number with the Newton polytope; we also characterize homology classes of $\mathbb {P}^n \times \mathbb {P}^m$ corresponding to subvarieties and answer a question posed by Trung-Verma.
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Additional Information
  • June Huh
  • Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
  • Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
  • MR Author ID: 974745
  • Email:,
  • Received by editor(s): July 10, 2011
  • Received by editor(s) in revised form: January 17, 2012
  • Published electronically: February 8, 2012
  • Additional Notes: The author acknowledges support from National Science Foundation grant DMS 0838434 “EMSW21-MCTP: Research Experience for Graduate Students”.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 25 (2012), 907-927
  • MSC (2010): Primary 14B05, 05B35
  • DOI:
  • MathSciNet review: 2904577