The neighborhood union of independent sets and hamiltonicity of graphs

Guantao Chen, Xuechao Li, Zhengsheng Wu, Xingping Xu
2007 Discrete Mathematics  
Let G be a graph, N (u) the neighborhood of u for each u ∈ V (G), and N(U) = u∈U N(u) for each U ⊆ V (G). For any two positive integers s and t, we prove that there exists a least positive integer N(s, t) such that every (s + t)-connected graph G of order n N(s, t) is hamiltonian if |N(S)| + |N(T )| n for every two disjoint independent vertex sets S, T with |S| = s and |T | = t.
doi:10.1016/j.disc.2006.10.010 fatcat:3ogwfqncrnhzbafvsuhibrx7qu