A note on dominating cycles in 2-connected graphs

D. Bauer, E. Schmeichel, H.J. Veldman
1996 Discrete Mathematics  
Let G be a 2-connected graph on n vertices such that d(x)+ d(y)+ d(z)>/n for all triples of independent vertices x,y,z. We prove that every longest cycle in G is a dominating cycle unless G is a spanning subgraph of a graph belonging to one of four easily specified classes of graphs.
doi:10.1016/0012-365x(94)00364-o fatcat:nrlvfrmodbcqhliq3xg2kr3joa