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Graph Theory pp 135–147Cite as

Chvátal’s t 0-Tough Conjecture

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Abstract

In 1973, Chvátal introduced the concept of “tough graphs” and conjectured that graphs with sufficiently high toughness are hamiltonian. Here we look at some personal perspectives of this conjecture, both those of Chvátal and the author. Furthermore, we present the history of the conjecture and its current status.

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Author information

Authors and Affiliations

  1. Western Michigan University, Kalamazoo, MI, USA

    Linda Lesniak

Authors
  1. Linda Lesniak
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Correspondence to Linda Lesniak .

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Editors and Affiliations

  1. Department of Applied Mathematics, Naval Postgraduate School, Monterey, California, USA

    Ralucca Gera

  2. School of Computing, Clemson University, Clemson, South Carolina, USA

    Stephen Hedetniemi

  3. Department of Mathematics, Virginia Commonwealth University, Richmond, Virginia, USA

    Craig Larson

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Lesniak, L. (2016). Chvátal’s t 0-Tough Conjecture. In: Gera, R., Hedetniemi, S., Larson, C. (eds) Graph Theory. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-31940-7_9

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