2 papers
math.CO2025
Minimally tough series-parallel graphs with toughness at least
Gyula Y. Katona, Humara Khan
Let be a positive real number. A graph is called \emph{-tough} if the removal of any vertex set that disconnects the graph leaves at most components. The toughne…
math.CO2025
On minimally tough chordal graphs
Clément Dallard, Blas Fernández, Gyula Y. Katona +2
Katona and Varga showed that for any rational number , no chordal graph is minimally -tough, while Katona and Khan characterized all minimally -tough, chordal…