A Diameter-Revealing Proof of the Bondy-Lovász Lemma
arXiv:1111.6561 · doi:10.1016/j.ipl.2021.106194
Abstract
We present a strengthened version of a lemma due to Bondy and Lovász. 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-Lovász 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.
arXiv comment8 pages, 1 figures