Morteza Saghafian
Edelsbrunner Group
11 Publications
2025 | Published | Journal Article | IST-REx-ID: 18626 |

Order-2 Delaunay triangulations optimize angles
H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).
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H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).
2024 | Submitted | Preprint | IST-REx-ID: 18999 |

Chromatic topological data analysis
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
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S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
2024 | Published | Conference Paper | IST-REx-ID: 17145 |

Grid peeling of parabolas
G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
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G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
2024 | Published | Conference Paper | IST-REx-ID: 15012 |

Decomposition of geometric graphs into star-forests
J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.
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J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.
2024 | Published | Conference Paper | IST-REx-ID: 18556 |

The Euclidean MST-ratio for bi-colored lattices
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
[Published Version]
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S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
2024 | Published | Journal Article | IST-REx-ID: 14345 |

On angles in higher order Brillouin tessellations and related tilings in the plane
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.
[Published Version]
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H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.
2024 | Published | Journal Article | IST-REx-ID: 15380 |

Depth in arrangements: Dehn–Sommerville–Euler relations with applications
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.
[Published Version]
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R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.
2024 | Published | Journal Article | IST-REx-ID: 13182 |

Geometric characterization of the persistence of 1D maps
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.
[Published Version]
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R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.
2024 | Draft | Preprint | IST-REx-ID: 15091 |

Chromatic alpha complexes
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
[Preprint]
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S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
2022 | Draft | Journal Article | IST-REx-ID: 11658 |

Depth in arrangements: Dehn–Sommerville–Euler relations with applications
Biswas, Ranita, Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics. 2022
[Submitted Version]
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Biswas, Ranita, Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics. 2022
2022 | Draft | Preprint | IST-REx-ID: 15090 |

On the size of chromatic Delaunay mosaics
R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
[Preprint]
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| arXiv
R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
Grants
11 Publications
2025 | Published | Journal Article | IST-REx-ID: 18626 |

Order-2 Delaunay triangulations optimize angles
H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).
[Preprint]
View
| DOI
| Download Preprint (ext.)
| WoS
| arXiv
H. Edelsbrunner, A. Garber, M. Saghafian, Advances in Mathematics 461 (2025).
2024 | Submitted | Preprint | IST-REx-ID: 18999 |

Chromatic topological data analysis
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
[Preprint]
View
| DOI
| Download Preprint (ext.)
| arXiv
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
2024 | Published | Conference Paper | IST-REx-ID: 17145 |

Grid peeling of parabolas
G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
[Published Version]
View
| Files available
| DOI
| arXiv
G. Rote, M. Rüber, M. Saghafian, in:, 40th International Symposium on Computational Geometry, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
2024 | Published | Conference Paper | IST-REx-ID: 15012 |

Decomposition of geometric graphs into star-forests
J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.
[Preprint]
View
| DOI
| Download Preprint (ext.)
| arXiv
J. Pach, M. Saghafian, P. Schnider, in:, 31st International Symposium on Graph Drawing and Network Visualization, Springer Nature, 2024, pp. 339–346.
2024 | Published | Conference Paper | IST-REx-ID: 18556 |

The Euclidean MST-ratio for bi-colored lattices
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
[Published Version]
View
| Files available
| DOI
| arXiv
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, in:, 32nd International Symposium on Graph Drawing and Network Visualization, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2024.
2024 | Published | Journal Article | IST-REx-ID: 14345 |

On angles in higher order Brillouin tessellations and related tilings in the plane
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.
[Published Version]
View
| Files available
| DOI
| WoS
| arXiv
H. Edelsbrunner, A. Garber, M. Ghafari, T. Heiss, M. Saghafian, Discrete and Computational Geometry 72 (2024) 29–48.
2024 | Published | Journal Article | IST-REx-ID: 15380 |

Depth in arrangements: Dehn–Sommerville–Euler relations with applications
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.
[Published Version]
View
| Files available
| DOI
| Download Published Version (ext.)
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 557–578.
2024 | Published | Journal Article | IST-REx-ID: 13182 |

Geometric characterization of the persistence of 1D maps
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.
[Published Version]
View
| Files available
| DOI
R. Biswas, S. Cultrera di Montesano, H. Edelsbrunner, M. Saghafian, Journal of Applied and Computational Topology 8 (2024) 1101–1119.
2024 | Draft | Preprint | IST-REx-ID: 15091 |

Chromatic alpha complexes
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
[Preprint]
View
| Files available
| DOI
| Download Preprint (ext.)
| arXiv
S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
2022 | Draft | Journal Article | IST-REx-ID: 11658 |

Depth in arrangements: Dehn–Sommerville–Euler relations with applications
Biswas, Ranita, Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics. 2022
[Submitted Version]
View
| Files available
Biswas, Ranita, Depth in arrangements: Dehn–Sommerville–Euler relations with applications. Leibniz International Proceedings on Mathematics. 2022
2022 | Draft | Preprint | IST-REx-ID: 15090 |

On the size of chromatic Delaunay mosaics
R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).
[Preprint]
View
| Files available
| Download Preprint (ext.)
| arXiv
R. Biswas, S. Cultrera di Montesano, O. Draganov, H. Edelsbrunner, M. Saghafian, ArXiv (n.d.).