A 4-cycle and a 2-factor with two components of a graph satisfying the Chvلtal-Erdِs condition

The condition that the independence number of a graph is less than or equal to its connectivity is called the Chvátal-Erdös condition. In this paper, we show the existence of a 2-factor with two components in a k(≥ 4)-connected graph satisfying the Chvátal-Erdös condition and having at least six vertices.