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Degrees, neighbourhoods and closure operations. (English) Zbl 0958.05073

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
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