On the shortness exponent of 1-tough, maximal planar graphs
The notion of shortness exponent of a family of graphs was introduced by \textit{B. Grünbaum} and \textit{H. Walther} [J. Comb. Theory, Ser. A 14, 364-385 (1973; Zbl 0263.05103)]. A graph \(G\) is said to be 1-tough if for any non-empty set \(S\) of vertices of \(G\), the number of components of \(G-S\) is smaller than the number of vertices in \(S\), see \textit{V. Chvátal} [Tough graphs and Hamiltonian circuits, Discrete Math. 5, 215-228 (1973; Zbl 0256.05122)]. In the paper of the author, a bound for the shortness exponent of a class of 1-tough planar graphs is presented.
scientific article; zbMATH DE number 906918