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arXiv · 1111.6561

A Diameter-Revealing Proof of the Bondy-Lov\'asz Lemma

Hyung-Chan An·Robert Kleinberg
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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 Gy\H{o}ri-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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Hyung-Chan An, Robert Kleinberg. 2011-11-28. A Diameter-Revealing Proof of the Bondy-Lov\'asz Lemma. https://doi.org/10.1016/j.ipl.2021.106194

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