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A Zero-Free Interval for Chromatic Polynomials of Graphs

  • Bill Jackson (a1)
Abstract

Let G be a graph and P(G, t) be the chromatic polynomial of G. It is known that P(G, t) has no zeros in the intervals (−∞, 0) and (0, 1). We shall show that P(G, t) has no zeros in (1, 32/27]. In addition, we shall construct graphs whose chromatic polynomials have zeros arbitrarily close to 32/27.

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[1]Birkhoff, G. D. and Lewis, D. C. (1946) Chromatic polynomials. Trans. Amer. Math. Soc. 60 355451.
[2]Tutte, W. T. (1966) Connectivity in Graphs, University of Toronto Press.
[3]Tutte, W. T. (1974) Chromials. Springer Lecture Notes in Mathematics 411 243266.
[4]Woodall, D. R. (1977) Zeros of chromatic polynomials. In: Cameron, P. (ed.) Combinatorial Surveys, Proc. Sixth British Combinatorial Conference, Academic Press, London199223.
[5]Woodall, D. R. (1992) A zero-free interval for chromatic polynomials. Discrete Math. 101 333341.
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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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