Fabrici, Igor; Hexel, Erhard; Jendrol, Stanislaw On vertices enforcing a Hamiltonian cycle. (English) Zbl 1293.05205 Discuss. Math., Graph Theory 33, No. 1, 71-89 (2013). Summary: A nonempty vertex set \(X\subseteq V(G)\) of a Hamiltonian graph \(G\) is called an \(H\)-force of \(G\) if every \(X\)-cycle of \(G\) (i.e. a cycle of \(G\) containing all vertices of \(X\)) is Hamiltonian. The \(H\)-force number \(h(G)\) of a graph \(G\) is defined to be the smallest cardinality of an \(H\)-force set of \(G\). In the paper the study of this parameter is introduced and its value or a lower bound for outerplanar graphs, planar graphs, \(k\)-connected graphs and prisms over graphs is determined. Cited in 5 Documents MSC: 05C45 Eulerian and Hamiltonian graphs 05C10 Planar graphs; geometric and topological aspects of graph theory Keywords:cycle; Hamiltonian; 1-Hamiltonian PDFBibTeX XMLCite \textit{I. Fabrici} et al., Discuss. Math., Graph Theory 33, No. 1, 71--89 (2013; Zbl 1293.05205) Full Text: DOI