Neighborhood conditions for balanced independent sets in bipartite graphs

AbstractLet G be a balanced bipartite graph of order 2n and minimum degree δ(G)⩾3. If, for every balanced independent set S of four vertices, |N(S)| > n then G is traceable, the circumference is at least 2n − 2 and G contains a 2-factor (with only small order exceptional graphs for the latter statement). If the neighborhood union condition is replaced by |N(S)| > n + 2 then G is hamiltonian