2026-08-11T08:05:04Z https://drops.dagstuhl.de/oai

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Short Topological Decompositions of Non-Orientable Surfaces Fuladi, Niloufar Hubard, Alfredo de Mesmay, Arnaud Computational topology embedded graph non-orientable surface joint crossing number canonical system of loop surface decomposition We investigate short topological decompositions of non-orientable surfaces and provide algorithms to compute them. Our main result is a polynomial-time algorithm that for any graph embedded in a non-orientable surface computes a canonical non-orientable system of loops so that any loop from the canonical system intersects any edge of the graph in at most 30 points. The existence of such short canonical systems of loops was well known in the orientable case and an open problem in the non-orientable case. Our proof techniques combine recent work of Schaefer-Štefankovič with ideas coming from computational biology, specifically from the signed reversal distance algorithm of Hannenhalli-Pevzner. This result confirms a special case of a conjecture of Negami on the joint crossing number of two embeddable graphs. We also provide a correction for an argument of Negami bounding the joint crossing number of two non-orientable graph embeddings. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Niloufar Fuladi and Alfredo Hubard and Arnaud de Mesmay 2022 Is Part Of LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SoCG.2022.41 urn:nbn:de:0030-drops-160492 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.41 eng https://creativecommons.org/licenses/by/4.0/legalcode