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Communication Dans Un Congrès Année : 2022

Short Topological Decompositions of Non-Orientable Surfaces

Résumé

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.

Dates et versions

hal-03713055 , version 1 (04-07-2022)

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Niloufar Fuladi, Alfredo Hubard, Arnaud de Mesmay. Short Topological Decompositions of Non-Orientable Surfaces. 38th International Symposium on Computational Geometry (SoCG 2022), Jun 2022, Berlin, Germany. ⟨10.4230/LIPIcs.SoCG.2022.41⟩. ⟨hal-03713055⟩
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