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Neighborhood conditions for balanced independent sets in bipartite graphs

Neighborhood conditions for balanced independent sets in bipartite graphs,10.1016/S0012-365X(97)00042-3,Discrete Mathematics,Denise Amar,Stephan Brand

Neighborhood conditions for balanced independent sets in bipartite graphs  
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Let 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.
Journal: Discrete Mathematics - DM , vol. 181, no. 1-3, pp. 31-36, 1998
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