The connectivities of leaf graphs of 2-connected graphs
Given a connected graph \(G=(V,E)\), its leaf graph \(\mathcal G\) has as vertex set the set of all spanning trees of \(G\); two vertices \(S\) and \(T\) of \(\mathcal G\) are adjacent exactly when there exists \(v\in V\) such that \(S-v=T-v\) is a connected subgraph of \(G\). Theorem: If \(G\) is biconnected with least valence \(\delta\), then \(\mathcal G\) is \((2\delta-2)\)-connected. Conjecture: If \(G\) is biconnected with \(\delta\geq 3\), then \(\mathcal G\) is hamiltonian.
scientific article; zbMATH DE number 1346957