An extended study of k-restricted edge connectivity: Another approach to Tait’s coloring theorem

Abstract

For a graph [Formula: see text], an edge connectivity [Formula: see text] is the minimum number of edges whose removal disconnects G. In this paper, we define property restricted edge connectivity. Then we appraise its particular case, more precisely k-restricted edge connectivity. Some of the basic properties of k-restricted edge connectivity are considered. We also discuss how k-restricted edge connectivity associates with graph coloring. In particular, we try to study how k-restricted edge connectivity relates with Tait’s coloring theorem and thereby the famous Four-color conjecture.