Discrete systolic inequalities and decompositions of triangulated surfaces

DOI10.1007/s00454-015-9679-9zbMath1314.05051arXiv1408.4036OpenAlexW2083650571MaRDI QIDQ2349858

Arnaud de Mesmay, Alfredo Hubard, Éric Colin de Verdière

Publication date: 18 June 2015

Published in: Discrete \& Computational Geometry, Proceedings of the thirtieth annual symposium on Computational geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.4036

zbMATH Keywords

surfaceRiemannian geometrysystolecomputational topologytriangulated surfacepants decompositionedge-widthtopological graph theoryclosed curvecut graphshortest non-trivial cycle

Mathematics Subject Classification ID

Graph theory (including graph drawing) in computer science (68R10) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Planar graphs; geometric and topological aspects of graph theory (05C10) Triangulating manifolds (57Q15) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Relations of low-dimensional topology with graph theory (57M15)

Related Items

Volume distortion in homotopy groups, Short cycles in high genus unicellular maps, Shortest path embeddings of graphs on surfaces, Filling triangulated surfaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Short loop decompositions of surfaces and the geometry of Jacobians
• Algorithms for the edge-width of an embedded graph
• Computing the shortest essential cycle
• Pants decompositions of random surfaces
• Explicit bounds for graph minors
• Automorphisms of random graphs with specified vertices
• Finding shortest non-separating and non-contractible cycles for topologically embedded graphs
• Splitting (complicated) surfaces is hard
• Filling Riemannian manifolds
• Graph minors. VII: Disjoint paths on a surface
• On the period matrix of a Riemann surface of large genus (with an appendix by J. H. Conway and N. J. A. Sloane)
• A simple construction of high representativity triangulations
• Optimally cutting a surface into a disk
• Asymptotic bounds for separating systoles on surfaces
• The length of closed geodesics on random Riemann surfaces
• Random construction of Riemann surfaces
• A manifold which does not admit any differentiable structure
• Untangling two systems of noncrossing curves
• Some inequalities in certain nonorientable Riemannian manifolds
• Multiple-Source Shortest Paths in Embedded Graphs
• THE STABILITY OF DELAUNAY TRIANGULATIONS
• Squarepants in a tree
• On a Lower Bound for Short Noncontractible Cycles in Embedded Graphs
• Optimal pants decompositions and shortest homotopic cycles on an orientable surface
• On Short Noncontractible Cycles in Embedded Graphs
• Sign and geometric meaning of curvature
• Homology Flows, Cohomology Cuts
• On Supporting High-Quality 3D Geometry Multicasting over IEEE 802.11 Wireless Networks
• Computing a canonical polygonal schema of an orientable triangulated surface
• Minimum cuts and shortest homologous cycles
• Tightening Nonsimple Paths and Cycles on Surfaces
• Topological characteristics of random triangulated surfaces
• Entropy of systolically extremal surfaces and asymptotic bounds
• Geometry and spectra of compact Riemann surfaces
• Riemannian geometry.