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

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

抄録

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.

本文言語英語
ホスト出版物のタイトルACM-SIAM Symposium on Discrete Algorithms, SODA 2022
出版社Association for Computing Machinery
ページ1342-1355
ページ数14
ISBN(電子版)9781611977073
出版ステータス出版済み - 2022
イベント33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022 - Alexander, 米国
継続期間: 1月 9 20221月 12 2022

出版物シリーズ

名前Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
2022-January

会議

会議33rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2022
国/地域米国
CityAlexander
Period1/9/221/12/22

!!!All Science Journal Classification (ASJC) codes

  • ソフトウェア
  • 数学 (全般)

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