An Ore-type condition for pancyclability
Let \(G\) be a graph of order \(n\) and \(S\) a subset of \(V(G)\). \(G\) is said to be \(S\)-pancyclable if for every integer \(l\) with \(3 \leq l \leq | S| \), there exists a cycle in \(G\) that contains exactly \(l\) vertices of \(S\). It is proved that if the degree sum in \(G\) is at least \(n\), then \(G\) is either \(S\)-pancyclable or else \(n\) is even, \(S = V(G)\) and \(G = K_{{n/2},{n/2}}\), or \(| S| = 4\), \(G[S] = K_{2,2}\) and the structure of \(G\) is well characterized.
scientific article; zbMATH DE number 1340371