A note on dominating cycles in 2-connected graphs
The authors and \textit{A. Morgana} [Discrete Math. 79, No. 1, 59-70 (1990; Zbl 0713.05041)] proved that in a 1-tough graph \(G\) on \(n\) vertices, with \(d(u)+d(v)+d(w)\geq n\) for all triples of independent vertices, every longest cycle is dominating. As an improvement, in the present paper this is essentially extended to the more general class of 2-connected graphs, by showing the following. Let \(G\) be a 2-connected graph with \(n\) vertices, with \(d(u)+d(v)+d(w)\geq n\) for all triples of independent vertices. Then every longest cycle is dominating, unless \(G\) is a spanning subgraph of a graph belonging to one of four special classes. These are explicitly described in the article.
scientific article; zbMATH DE number 932520
scientific article