Neighborhood unions and hamiltonicity of graphs
If \(G\) is a 2-connected graph of order \(n\) such that the union of the neighborhoods of each pair of vertices that are a distance 2 apart is at least \((n+ 2)/3\), then \(G\) is either hamiltonian or belongs to one of three exceptional classes of graphs (all of which are 2-connected). This generalizes a result of \textit{B. Jackson} [J. Graph Theory 15, No. 4, 443- 451 (1991; Zbl 0739.05058)] in which the same neighborhood condition was used for all nonadjacent pairs of vertices.
scientific article; zbMATH DE number 778537