The structure of minimally [formula omitted]-tough, [formula omitted]-free graphs.

A graph G is minimally t -tough if the toughness of G is t and deletion of any edge from G decreases its toughness. Kriesell conjectured that the minimum degree of a minimally 1-tough graph is 2, and Katona et al. proposed a generalized version of the conjecture that the minimum degree of a minimally t -tough graph is ⌈ 2 t ⌉. In this paper, we characterize the minimally 1 / a -tough, 2 K 2 -free graphs for an integer a. [ABSTRACT FROM AUTHOR]