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# Discrete Systolic Inequalities and Decompositions of Triangulated Surfaces

@inproceedings{Verdire2014DiscreteSI, title={Discrete Systolic Inequalities and Decompositions of Triangulated Surfaces}, author={{\'E}ric Colin de Verdi{\`e}re and Alfredo Hubard and Arnaud de Mesmay}, booktitle={Symposium on Computational Geometry}, year={2014} }

- Published 2014 in Symposium on Computational Geometry
DOI:10.1145/2582112.2582127

How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial closed curves, pants decompositions, and cut graphs with a given combinatorial map in triangulated combinatorial surfaces (or their dual cross-metric counterpart).
Our work builds upon Riemannian systolic inequalities, which bound the minimum length of non-trivial closed curves in terms of the genus and the area of the… CONTINUE READING

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