Vertex-deleted subgraphs and regular factors from regular graph

Abstract

Let k , m , and r be three integers such that 2 ≤ k ≤ m ≤ r . Let G be a 2 r -regular, 2 m -edge-connected graph of odd order. We obtain some sufficient conditions for G − v to contain a k -factor for all v ∈ V ( G ) .