Two Approaches for the Generalization of Leaf Edge Exchange Graphs on Spanning Trees to Connected Spanning \(k\)-Edge Subgraphs of a Graph

Abstract

In a paper of Harary and Plantholt, they concluded by noting that they knew of no generalization of the leaf edge exchange (\(LEE\)) transition sequence result on spanning trees to other natural families of spanning subgraphs. Now, we give two approaches for such a generalization. We define two kinds of \(LEE\)-graphs over the set of all connected spanning \(k\)-edge subgraphs of a connected graph \(G\), and show that both of them are connected for a \(2\)-connected graph \(G\).