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Algorithms"],"published-print":{"date-parts":[[2023,1,31]]},"abstract":"<jats:p>\n            We initiate the study of\n            <jats:italic>k<\/jats:italic>\n            -edge-connected orientations of undirected graphs through edge flips for\n            <jats:italic>k<\/jats:italic>\n            \u2265 2. We prove that in every orientation of an undirected\n            <jats:italic>2k<\/jats:italic>\n            -edge-connected graph, there exists a sequence of edges such that flipping their directions one by one does not decrease the edge connectivity, and the final orientation is\n            <jats:italic>k<\/jats:italic>\n            -edge connected. This yields an \u201cedge-flip based\u201d new proof of Nash-Williams\u2019 theorem: A undirected graph\n            <jats:italic>G<\/jats:italic>\n            has a\n            <jats:italic>k<\/jats:italic>\n            -edge-connected orientation if and only if\n            <jats:italic>G<\/jats:italic>\n            is\n            <jats:italic>2k<\/jats:italic>\n            -edge connected. As another consequence of the theorem, we prove that the edge-flip graph of\n            <jats:italic>k<\/jats:italic>\n            -edge-connected orientations of an undirected graph\n            <jats:italic>G<\/jats:italic>\n            is connected if\n            <jats:italic>G<\/jats:italic>\n            is\n            <jats:italic>(2k+2)<\/jats:italic>\n            -edge connected. This has been known to be true only when\n            <jats:italic>k=1<\/jats:italic>\n            .\n          <\/jats:p>","DOI":"10.1145\/3561302","type":"journal-article","created":{"date-parts":[[2022,9,6]],"date-time":"2022-09-06T11:53:46Z","timestamp":1662465226000},"page":"1-22","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":5,"title":["Monotone Edge Flips to an Orientation of Maximum Edge-Connectivity \u00e0 la Nash-Williams"],"prefix":"10.1145","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9912-6898","authenticated-orcid":false,"given":"Takehiro","family":"Ito","sequence":"first","affiliation":[{"name":"Graduate School of Information Sciences, Tohoku University, Aramaki-aza, Aoba-ku, Sendai, Miyagi, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6794-3543","authenticated-orcid":false,"given":"Yuni","family":"Iwamasa","sequence":"additional","affiliation":[{"name":"Graduate School of Informatics, Kyoto University, Yoshida Honmachi, Sakyo-ku, Kyoto, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3918-3479","authenticated-orcid":false,"given":"Naonori","family":"Kakimura","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, Keio University, Hiyoshi, Kohoku-ku, Yokohama, Kanagawa, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7712-2730","authenticated-orcid":false,"given":"Naoyuki","family":"Kamiyama","sequence":"additional","affiliation":[{"name":"Institute of Mathematics for Industry, Kyushu University, Nishi-ku, Fukuoka, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9478-7307","authenticated-orcid":false,"given":"Yusuke","family":"Kobayashi","sequence":"additional","affiliation":[{"name":"Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1607-8665","authenticated-orcid":false,"given":"Shun-Ichi","family":"Maezawa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Tokyo University of Science, Shijuku-ku, Tokyo, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3223-0153","authenticated-orcid":false,"given":"Yuta","family":"Nozaki","sequence":"additional","affiliation":[{"name":"Graduate School of Advanced Science and Engineering, Hiroshima University, Hiroshima, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9826-7074","authenticated-orcid":false,"given":"Yoshio","family":"Okamoto","sequence":"additional","affiliation":[{"name":"Graduate School of Informatics and Engineering, The University of Electro-Communications, Chofu, Tokyo, Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3118-0086","authenticated-orcid":false,"given":"Kenta","family":"Ozeki","sequence":"additional","affiliation":[{"name":"Faculty of Environment and Information Sciences, Yokohama National University, Hodogaya-ku, Yokohama, Japan"}]}],"member":"320","published-online":{"date-parts":[[2023,2,20]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-020-00751-1"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.20158"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.disopt.2008.03.001"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2013.11.003"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2019.07.001"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(08)72446-0"},{"key":"e_1_3_2_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(82)90044-9"},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511662089.005"},{"key":"e_1_3_2_10_2","first-page":"111","volume-title":"Handbook of Combinatorics","author":"Frank Andr\u00e1s","year":"1996","unstructured":"Andr\u00e1s Frank. 1996. 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