A diameter-revealing proof of the Bondy-Lovász lemma

Hyung Chan An; Robert Kleinberg

doi:10.1016/j.ipl.2021.106194

A diameter-revealing proof of the Bondy-Lovász lemma

Hyung Chan An, Robert Kleinberg

College of Computing

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	106194
Journal	Information Processing Letters
Volume	174
DOIs	https://doi.org/10.1016/j.ipl.2021.106194
Publication status	Published - 2022 Mar

Bibliographical note

Funding Information:
Research supported in part by NSF under grants no. CCF-1017688 and CCF-0729102, and the Korea Foundation for Advanced Studies. Part of this research was conducted while the author was a PhD student at Cornell University. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1C1C1008934).Supported by NSF grants CCF-0643934 and CCF-0729102, AFOSR grant FA9550-09-1-0100, a Microsoft Research New Faculty Fellowship, a Google Research Grant, and an Alfred P. Sloan Foundation Fellowship.

Publisher Copyright:
© 2021 Elsevier B.V.

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/j.ipl.2021.106194

Cite this

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title = "A diameter-revealing proof of the Bondy-Lov{\'a}sz lemma",

abstract = "We present a strengthened version of a lemma due to Bondy and Lov{\'a}sz. 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{\'a}sz 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.",

author = "An, {Hyung Chan} and Robert Kleinberg",

note = "Funding Information: Research supported in part by NSF under grants no. CCF-1017688 and CCF-0729102, and the Korea Foundation for Advanced Studies. Part of this research was conducted while the author was a PhD student at Cornell University. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1C1C1008934).Supported by NSF grants CCF-0643934 and CCF-0729102, AFOSR grant FA9550-09-1-0100, a Microsoft Research New Faculty Fellowship, a Google Research Grant, and an Alfred P. Sloan Foundation Fellowship. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

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A diameter-revealing proof of the Bondy-Lovász lemma

Abstract

Bibliographical note

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