Hamiltonicity of 4-connected graphs.

Let σ κ( G) denote the minimum degree sum of k independent vertices in G and α( G) denote the number of the vertices of a maximum independent set of G. In this paper we prove that if G is a 4-connected graph of order n and σ5( G) ≥ n + 3 α( G) + 11, then G is Hamiltonian. [ABSTRACT FROM AUTHOR]