An inequality for Tutte polynomials

Abstract

Let G be a graph without loops or bridges and a, b be positive real numbers with ba(a+2). We show that the Tutte polynomial of G satisfies the inequality T G (b, 0)T G (0, b) ≥ T G (a, a)2. Our result was inspired by a conjecture of Merino and Welsh that T G (1, 1) ≤ max{T G (2, 0),T G (0, 2)}.

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Correspondence to Bill Jackson.

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Jackson, B. An inequality for Tutte polynomials. Combinatorica 30, 69–81 (2010). https://doi.org/10.1007/s00493-010-2484-4

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Mathematics Subject Classification (2000)

  • 05C31
  • 05B35