Graphs and Combinatorics

, Volume 22, Issue 1, pp 1–35

Toughness in Graphs – A Survey


    • Department of Mathematical SciencesStevens Institute of Technology
  • Hajo Broersma
    • Department of Computer ScienceUniversity of Durham
    • Center for CombinatoricsNankai University
  • Edward Schmeichel
    • Department of MathematicsSan Jose State University

DOI: 10.1007/s00373-006-0649-0

Cite this article as:
Bauer, D., Broersma, H. & Schmeichel, E. Graphs and Combinatorics (2006) 22: 1. doi:10.1007/s00373-006-0649-0


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!


Toughnesst-tough graphHamilton cycleHamiltonian graphTraceable graphCircumferenceFactork-factorChordal graphTriangle-free graphPlanar graphComputational complexity

Copyright information

© Springer-Verlag Berlin Heidelberg 2006