Graphs and Combinatorics

, Volume 22, Issue 1, pp 1–35 | Cite as

Toughness in Graphs – A Survey

Article

Abstract

In this survey we have attempted to bring together most of the results and papers that deal with toughness related to cycle structure. We begin with a brief introduction and a section on terminology and notation, and then try to organize the work into a few self explanatory categories. These categories are circumference, the disproof of the 2-tough conjecture, factors, special graph classes, computational complexity, and miscellaneous results as they relate to toughness. We complete the survey with some tough open problems!

Keywords

Toughness t-tough graph Hamilton cycle Hamiltonian graph Traceable graph Circumference Factor k-factor Chordal graph Triangle-free graph Planar graph Computational complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Douglas Bauer
    • 1
  • Hajo Broersma
    • 2
    • 4
  • Edward Schmeichel
    • 3
  1. 1.Department of Mathematical SciencesStevens Institute of TechnologyHobokenUSA
  2. 2.Department of Computer ScienceUniversity of DurhamDurhamUK
  3. 3.Department of MathematicsSan Jose State UniversitySan JoseUSA
  4. 4.Center for CombinatoricsNankai UniversityTianjinP.R. China

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