Notice of RetractionSome sufficient and necessary conditions for defect n-extendable graphs

Notice of Retraction

After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.

We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.

The presenting author of this paper has the option to appeal this decision by contacting TPII@ieee.org.

A near perfect matching is a matching covering all but one vertex in a graph. Let G be a connected graph and n≤(|V (G)|-2)/2 be a positive integer. If any n independent edges in G are contained in a near perfect matching, then G is said to be defect n-extendable. In this paper, we first show that if G is a graph with odd order and δ(G) ≥ (|V (G)| - 1)/2 + n, then G is defect n-extendable. We also construct a graph to show that the bound for δ(G) is sharp. Then we give a characterization of defect n-extendable graph and some properties of defect 1-extendable graphs.