A diameter-revealing proof of the Bondy-Lovász lemma

Abstract We present a strengthened version of a lemma due to Bondy and Lovasz. This lemma establishes the connectivity of a certain graph whose nodes correspond to the spanning trees of a 2-vertex-connected graph, and implies the k = 2 case of the Győri-Lovasz Theorem on partitioning of k-vertex-connected graphs. Our strengthened version constructively proves an asymptotically tight O ( | V | 2 ) bound on the worst-case diameter of this graph of spanning trees.