A diameter-revealing proof of the Bondy-Lovasz lemma

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 Gyori-Lovasz Theorem on partitioning of k-vertex-connected graphs. Our strengthened version constructively proves an asymptotically tight O(vertical bar V vertical bar(2)) bound on the worst-case diameter of this graph of spanning trees. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

We present a strengthened version of a lemma by Bondy and Lovasz, which establishes the connectivity of a graph of spanning trees and proves an asymptotically tight bound on the worst-case diameter.