{"pk":64820,"title":"Even circuits in oriented matroids","subtitle":null,"abstract":"In this paper we generalise the even directed cycle problem, which asks whether a given digraph contains a directed cycle of even length, to orientations of regular matroids. We define non-even oriented matroids generalising non-even digraphs, which played a central role in resolving the computational complexity of the even dicycle problem. Then we show that the problem of detecting an even directed circuit in a regular matroid is polynomially equivalent to the recognition of non-even oriented matroids. Our main result is a precise characterisation of the class of non-even oriented cographic matroids in terms of forbidden minors, which complements an existing characterisation of non-even oriented graphic matroids by Seymour and Thomassen.\n \nMathematics Subject Classifications: 05B35, 05C20, 05C70, 05C75, 05C83, 05C85, 52C40","language":"en","license":{"name":"Creative Commons Attribution 4.0","short_name":"CC BY 4.0","text":"Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.\n\nNo additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.","url":"https://creativecommons.org/licenses/by/4.0"},"keywords":[{"word":"Oriented matroids"},{"word":"circuits"},{"word":"even cycle problem"},{"word":"regular matroids"}],"section":"Research Articles","is_remote":true,"remote_url":"https://escholarship.org/uc/item/95h763tz","frozenauthors":[{"first_name":"Karl","middle_name":"","last_name":"Heuer","name_suffix":"","institution":"Technische Universität Berlin, Institute of Software Engineering and Theoretical Computer Science, Berlin, Germany","department":""},{"first_name":"Raphael","middle_name":"","last_name":"Steiner","name_suffix":"","institution":"Technische Universität Berlin, Institute of Mathematics, Berlin, Germany","department":""},{"first_name":"Sebastian","middle_name":"","last_name":"Wiederrecht","name_suffix":"","institution":"Technische Universität Berlin, Institute of Software Engineering and Theoretical Computer Science, Berlin, Germany","department":""}],"date_submitted":"2022-03-23T19:45:28Z","date_accepted":"2022-03-23T19:45:28Z","date_published":"2022-03-31T07:00:00Z","render_galley":null,"galleys":[{"label":"","type":"pdf","path":"https://journalpub.escholarship.org/combinatorial_theory/article/64820/galley/49630/download/"}]}