Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-98-06

May 1998

The Complexity of Toughness in Regular Graphs

D.Bauer, J. van den Heuvel, A. Morgana, and E. Schmeichel


Let  t >= 1  be an integer. We show that it is NP-hard to determine if an r-regular graph is t-tough for any fixed integer  r >= 3t.  We also discuss the complexity of recognizing if an r-regular graph is t-tough, for any rational  t >= 1.

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