Minimal toughness in special graph classes.

Let t be a positive real number. A graph is called t-tough if the removal of any vertex set S that disconnects the graph leaves at most |S|/t components, and all graphs are considered 0-tough. The toughness of a graph is the largest t for which the graph is t-tough, whereby the toughness of complete graphs is defined as infinity. A graph is minimally t-tough if the toughness of the graph is t, and the deletion of any edge from the graph decreases the toughness. In this paper, we investigate the minimum degree and the recognizability of minimally t-tough graphs in the classes of chordal graphs, split graphs, claw-free graphs, and 2K2-free graphs. [ABSTRACT FROM AUTHOR]