A Characterization of 3-Tough Cubic Graphs

Bill Jackson1, P. Katerinis2
1Department of Mathematical Studies Goldsmiths’ College London SE14 6NW, England
2Department of Informatics Athens University of Economics and Business Athens, 10434 Greece

Abstract

We show that a cubic graph is \(\frac{3}{2}\)-tough if and only if it is equal to \(K_4\) or \(K_3 \times K_3\) or else is the inflation of a 3-connected cubic graph.