Binomial Inequalities for Chromatic, Flow, and Tension Polynomials

  title={Binomial Inequalities for Chromatic, Flow, and Tension Polynomials},
  author={Matthias Beck and Emerson Leon},
  journal={Discret. Comput. Geom.},
  • M. Beck, E. Leon
  • Published 31 March 2018
  • Mathematics, Computer Science
  • Discret. Comput. Geom.
A famous and wide-open problem, going back to at least the early 1970’s, concerns the classification of chromatic polynomials of graphs. Toward this classification problem, one may ask for necessary inequalities among the coefficients of a chromatic polynomial, and we contribute such inequalities when a chromatic polynomial χG(n) = χ ∗ 0 ( n+d d ) + χ∗ 1 ( n+d−1 d ) + · · ·+ χ∗ d ( n d ) is written in terms of a binomial-coefficient basis. For example, we show that χj ≤ χ ∗ d− j , for 0 ≤ j ≤ d… 


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