Monotone edge ips to an orientation of maximum edge-connectivity a la Nash-Williams

Takehiro Ito, Yuni Iwamasa, Naonori Kakimura, Naoyuki Kamiyama, Yusuke Kobayashi, Shun Ichi Maezawa, Yuta Nozaki, Yoshio Okamoto, Kenta Ozeki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We initiate the study of k-edge-connected orientations of undirected graphs through edge ips for k 2. We prove that in every orientation of an undirected 2k-edge-connected graph, there exists a sequence of edges such that ipping their directions one by one does not decrease the edge-connectivity, and the final orientation is k-edge-connected. This yields an \edge-ip based"new proof of Nash-Williams' theorem: an undirected graph G has a k-edge-connected orientation if and only if G is 2k-edge-connected. As another consequence of the theorem, we prove that the edge-ip graph of k-edge-connected orientations of an undirected graph G is connected if G is (2k + 2)-edge-connected. This has been known to be true only when k = 1.

Original languageEnglish
Title of host publicationACM-SIAM Symposium on Discrete Algorithms, SODA 2022
PublisherAssociation for Computing Machinery
Pages1342-1355
Number of pages14
ISBN (Electronic)9781611977073
Publication statusPublished - 2022
Event33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 - Alexander, United States
Duration: 2022 Jan 92022 Jan 12

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
Volume2022-January

Conference

Conference33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
Country/TerritoryUnited States
CityAlexander
Period22/1/922/1/12

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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