Stacho, L. Degrees, neighbourhoods and closure operations. (English) Zbl 0958.05073 Acta Math. Univ. Comen., New Ser. 69, No. 1, 71-76 (2000). Author’s summary: Closure theorems in graph theory are of the following type: Let \(G\) be a graph, \(P\) a graph-theoretic property, and let \(u\) and \(v\) be two nonadjacent vertices of \(G\). If condition \(c(u,v)\) holds, then \(G\) has property \(P\) if and only if \(G+ uv\) has property \(P\). We discuss several results of the above type where the condition \(c(u,v)\) refers to neighbourhood properties of \(u\) and \(v\). Reviewer: C.Lai (Zhangzhou) MSC: 05C38 Paths and cycles 05C45 Eulerian and Hamiltonian graphs Keywords:closure; graph-theoretic property; neighbourhood PDFBibTeX XMLCite \textit{L. Stacho}, Acta Math. Univ. Comen., New Ser. 69, No. 1, 71--76 (2000; Zbl 0958.05073) Full Text: EuDML EMIS