Long cycles through specified vertices in a graph (Q1262323)

The author shows the existence of a circuit of length at least \(((k- m)/k)\ell +2m\) containing m, \(0\leq m\leq k\), prescribed vertices of a k- connected graph G, \(k\geq 2\), generalizing a result of Dirac \((k=m)\). \(\ell\) denotes the maximum length of a circuit on G. He also proves analogous results for k-regular k-connected and for 3-connected planar graphs.