A Diameter-Revealing Proof of the Bondy-Lov\'asz Lemma
Abstract
We present a strengthened version of a lemma due to Bondy and Lov\'asz. 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 Gyori-Lov\'asz 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.
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