Toughness and binding number

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Abstract

Let τ(G) and bind(G) be the toughness and binding number, respectively, of a graph G. Woodall observed in 1973 that τ(G)≥bind(G)-1. In this paper, we obtain best possible improvements of this inequality except when (1+5)/2<bind(G)<2 and bind(G) has even denominator when expressed in lowest terms. © 2013 Elsevier B.V. All rights reserved.

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Bauer, D., Kahl, N., Schmeichel, E., Woodall, D. R., & Yatauro, M. (2014). Toughness and binding number. Discrete Applied Mathematics, 165, 60–68. https://doi.org/10.1016/j.dam.2012.08.007

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