Minimally tough chordal graphs with toughness at most 1/2

• DOI: 10.1016/j.disc.2023.113491
• Publication Date: 2023-05-05T21:19:39Z
• Authors: Gyula Y. Katona; Humara Khan
• Keywords: Interval graph; Split graph; Corollary; Outerplanar graph

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