This paper introduces an Ishikawa type iterative algorithm for finding approximating solutions of a class of multi-valued variational inclusion problems. Characterization of strong convergence of this iterative method is established. Copyright Springer-Verlag 2009

We introduce a new class of graphs which we call P <Subscript>3</Subscript>-dominated graphs. This class properly contains all quasi-claw-free graphs, and hence all claw-free graphs. Let G be a 2-connected P <Subscript>3</Subscript>-dominated graph. We prove that G is hamiltonian if α(G <Superscript>2</Superscript>) ≤ κ(G), with two exceptions: K <Subscript>2,3</Subscript> and K <Subscript>1,1,3</Subscript>....</subscript></subscript></superscript></subscript></subscript>