  Let $t$ be a positive real number. A graph is called \emph{$t$-tough} if the
removal of any vertex set $S$ that disconnects the graph leaves at most $|S|/t$
components. The toughness of a graph is the largest $t$ for which the graph is
$t$-tough. 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. A graph is
\emph{chordal} if it does not contain an induced cycle of length at least $4$.
  We characterize the minimally $t$-tough, chordal graphs for all $t\le 1/2$.
As a corollary, a characterization of minimally $t$-tough, interval graphs is
obtained for $t\le 1/2$.

Combinatorics;Discrete Mathematics