Georg Grasegger

Dr.

Georg Grasegger

Dr.

Senior Research Scientist
Symbolic Computation

+43 732 2468 5270
Georg.Grasegger(at)oeaw.ac.at

https://orcid.org/0000-0001-7421-8115

Research interests

Rigidity Theory
Symbolic Computation
Algebraic Geometry
Algebraic Differential Equations

Publications

Single-cell 3D genome reconstruction in the haploid setting using rigidity theory
Single-cell 3D genome reconstruction in the haploid setting using rigidity theory. / Dewar, Sean; Grasegger, Georg; Kubjas, Kaie et al.
in: Journal of Mathematical Biology, Jahrgang 90, Nr. 4, 45, 04.2025, S. 45.
DOI RIS ENW BIB
On the uniqueness of collections of pennies and marbles
On the uniqueness of collections of pennies and marbles. / Dewar, Sean; Grasegger, Georg; Kubjas, Kaie et al.
in: Examples and Counterexamples, Jahrgang 7, 14.02.2025, S. 100181.
DOI RIS ENW BIB
The number of realisations of a rigid graph in Euclidean and spherical geometries
The number of realisations of a rigid graph in Euclidean and spherical geometries. / Dewar, Sean; Grasegger, Georg.
in: Algebraic Combinatorics, Jahrgang 7, Nr. 6, 31.12.2024, S. 1615-1645.
DOI RIS ENW BIB
Quotient graphs of symmetrically rigid frameworks
Quotient graphs of symmetrically rigid frameworks. / Dewar, Sean; Grasegger, Georg; Kastis, Eleftherios et al.
in: Documenta Mathematica, Jahrgang 29, Nr. 3, 08.05.2024, S. 561-595.
DOI RIS ENW BIB
Flexibility and rigidity of frameworks consisting of triangles and parallelograms
Flexibility and rigidity of frameworks consisting of triangles and parallelograms. / Grasegger, Georg; Legerský, Jan.
in: Computational Geometry: Theory and Applications, Jahrgang 120, 19.02.2024, S. 102055.
DOI RIS ENW BIB
Coupler curves of moving graphs and counting realizations of rigid graphs
Coupler curves of moving graphs and counting realizations of rigid graphs. / Grasegger, Georg; Hilany, El; Lubbes, Niels.
in: Mathematics of Computation, Jahrgang 93, 01.01.2024, S. 459-504.
DOI RIS ENW BIB
Graph Rigidity Properties of Ramanujan Graphs
Graph Rigidity Properties of Ramanujan Graphs. / Cioabă, Sebastian M; Dewar, Sean; Grasegger, Georg et al.
in: Electronic Journal of Combinatorics, Jahrgang 30, Nr. 3, 28.07.2023, S. P3.12.
DOI RIS ENW BIB
Minimal counterexamples to Hendrickson's conjecture on globally rigid graphs
Minimal counterexamples to Hendrickson's conjecture on globally rigid graphs. / Grasegger, Georg.
in: Examples and Counterexamples, Jahrgang 3, 06.04.2023, S. 100106.
DOI RIS ENW BIB
Bracing frameworks consisting of parallelograms
Bracing frameworks consisting of parallelograms. / Grasegger, Georg; Legerský, Jan.
in: Art of Discrete and Applied Mathematics, Jahrgang 5, Nr. 2, 11.05.2022, S. P2.03:1-21.
DOI RIS ENW BIB
Flexible circuits in the d-dimensional rigidity matroid
Flexible circuits in the d-dimensional rigidity matroid. / Grasegger, Georg; Guler, Hakan; Jackson, Bill et al.
in: Journal of Graph Theory, Jahrgang 100, Nr. 2, 08.04.2022, S. 315-330.
DOI RIS ENW BIB
Zero-sum cycles in flexible polyhedra
Zero-sum cycles in flexible polyhedra. / Gallet, Matteo; Grasegger, Georg; Legerský, Jan et al.
in: Bulletin of the London Mathematical Society, Jahrgang 54, Nr. 1, 04.03.2022, S. 112-125.
DOI Download RIS ENW BIB
On the existence of paradoxical motions of generically rigid graphs on the sphere
On the existence of paradoxical motions of generically rigid graphs on the sphere. / Gallet, Matteo; Grasegger, Georg; Legerský, Jan et al.
in: SIAM Journal on Discrete Mathematics, Jahrgang 35, Nr. 1, 12.03.2021, S. 325-361.
DOI RIS ENW BIB
Combinatorics of Bricard's octahedra
Combinatorics of Bricard's octahedra. / Gallet, Matteo; Grasegger, Georg; Legerský, Jan et al.
in: Comptes Rendus Mathematique, Jahrgang 359, Nr. 1, 02.03.2021, S. 7-38.
DOI RIS ENW BIB
On the Classification of Motions of Paradoxically Movable Graphs
On the Classification of Motions of Paradoxically Movable Graphs. / Grasegger, Georg; Legerský, Jan; Schicho, Josef.
in: Journal of Computational Geometry, Jahrgang 11, Nr. 1, 15.12.2020, S. 548-575.
DOI RIS ENW BIB
Graphs with Flexible Labelings allowing Injective Realizations
Graphs with Flexible Labelings allowing Injective Realizations. / Grasegger, Georg; Legerský, Jan; Schicho, Josef.
in: Discrete Mathematics, Jahrgang 343, Nr. 6, 01.06.2020, S. 1-14.
DOI RIS ENW BIB
Lower bounds on the number of realizations of rigid graphs
Lower bounds on the number of realizations of rigid graphs. / Grasegger, Georg; Koutschan, Christoph; Tsigaridas, Elias.
in: Experimental Mathematics, Jahrgang 29, Nr. 2, 20.05.2020, S. 125-136.
DOI RIS ENW BIB
Counting realizations of Laman graphs on the sphere
Counting realizations of Laman graphs on the sphere. / Gallet, Matteo; Grasegger, Georg; Schicho, Josef.
in: Electronic Journal of Combinatorics, Jahrgang 27, Nr. 2, 03.04.2020, S. P2.5 (1-18).
DOI RIS ENW BIB
Graphs with Flexible Labelings
Graphs with Flexible Labelings. / Grasegger, Georg; Legerský, Jan; Schicho, Josef.
in: Discrete and Computational Geometry, Jahrgang 62, Nr. 2, 05.08.2019, S. 461-480.
DOI RIS ENW BIB
Computation of all rational solutions of first-order algebraic ODEs
Computation of all rational solutions of first-order algebraic ODEs. / Vo, Thieu N; Grasegger, Georg; Winkler, Franz.
in: Advances in Applied Mathematics, Jahrgang 98, 01.07.2018, S. 1-24.
DOI RIS ENW BIB
Deciding the existence of rational general solutions for first-order algebraic ODEs
Deciding the existence of rational general solutions for first-order algebraic ODEs. / Vo, Thieu N; Grasegger, Georg; Winkler, Franz.
in: Journal of Symbolic Computation, Jahrgang 87, 01.07.2018, S. 127-139.
DOI RIS ENW BIB
Rational General Solutions of Systems of First-Order Partial Differential Equations
Rational General Solutions of Systems of First-Order Partial Differential Equations. / Grasegger, Georg; Lastra, Alberto; Sendra, J Rafael et al.
in: Journal of Computational and Applied Mathematics, Nr. 331, 15.03.2018, S. 88-103.
DOI RIS ENW BIB
The number of realizations of a Laman graph
The number of realizations of a Laman graph. / Capco, Jose; Gallet, Matteo; Grasegger, Georg et al.
in: SIAM Journal on Applied Algebra and Geometry, Jahrgang 2, Nr. 1, 06.03.2018, S. 94-125.
DOI Website RIS ENW BIB
Computing the number of realizations of a Laman graph
Computing the number of realizations of a Laman graph. / Capco, Jose; Gallet, Matteo; Grasegger, Georg et al.
in: Electronic Notes in Discrete Mathematics, Jahrgang 61, 03.08.2017, S. 207-213.
DOI Website RIS ENW BIB
A solution method for autonomous first-order algebraic partial differential equations
A solution method for autonomous first-order algebraic partial differential equations. / Grasegger, Georg; Lastra, Alberto; Sendra, J Rafael et al.
in: Journal of Computational and Applied Mathematics, Jahrgang 300, 18.01.2016, S. 119--133.
DOI Website RIS ENW BIB

Flexible Placements of Graphs with Rotational Symmetry
Flexible Placements of Graphs with Rotational Symmetry. / Dewar, Sean; Grasegger, Georg; Legerský, Jan et al.
2nd IMA Conference on Mathematics of Robotics. Springer, Cham, 2022. S. 89-97 (Springer Proceedings in Advanced Robotics).
DOI Download RIS ENW BIB
Zero-Sum Cycles in Flexible Non-triangular Polyhedra
Zero-Sum Cycles in Flexible Non-triangular Polyhedra. / Gallet, Matteo; Grasegger, Georg; Legerský, Jan et al.
2nd IMA Conference on Mathematics of Robotics. Springer, Cham, 2022. S. 137-143 (Springer Proceedings in Advanced Robotics).
DOI Download RIS ENW BIB
FlexRiLoG—A SageMath Package for Motions of Graphs
FlexRiLoG—A SageMath Package for Motions of Graphs. / Grasegger, Georg; Legerský, Jan; Bigatti, Anna Maria (Herausgeber:in) et al.
Mathematical Software – ICMS 2020. 2020. S. 442-450 (Lecture Notes in Computer Science).
DOI RIS ENW BIB
Computing Animations of Linkages with Rotational Symmetry
Computing Animations of Linkages with Rotational Symmetry. / Dewar, Sean; Grasegger, Georg; Legerský, Jan.
36th International Symposium on Computational Geometry (SoCG 2020). 2020. (Leibniz International Proceedings in Informatics (LIPIcs)).
DOI RIS ENW BIB
Animated Motions of Exceptional Flexible Instances of Generically Rigid Graphs
Animated Motions of Exceptional Flexible Instances of Generically Rigid Graphs. / Grasegger, Georg; Legerský, Jan; Schicho, Josef.
Bridges Linz 2019 Conference Proceedings. Tessellations Publishing, 2019. S. 255–262.
Website Download RIS ENW BIB
Realizations and Constructions of Minimally Rigid Graphs
Realizations and Constructions of Minimally Rigid Graphs. / Grasegger, Georg.
Bridges Stockholm 2018 Conference Proceedings. Tessellations Publishing, 2018. S. 239-242.
DOI Website RIS ENW BIB
An Algebraic-Geometric Method for Computing Zolotarev Polynomials
An Algebraic-Geometric Method for Computing Zolotarev Polynomials. / Grasegger, Georg; Vo, Thieu N; Burr, Michael (Herausgeber:in).
Proceedings of the 2017 ACM. Kaiserslautern: ACM, 2017. S. 173-180 (ISSAC '17).
DOI RIS ENW BIB
A decision algorithm for rational general solutions of first-order algebraic ODEs
A decision algorithm for rational general solutions of first-order algebraic ODEs. / Grasegger, Georg; Vo, Thieu N; Winkler, Franz.
XV Encuentro de Álgebra computacional y aplicaciones. Logroño, 2016. S. 101-104.
RIS ENW BIB

Explorations on the number of realizations of minimally rigid graphs
Explorations on the number of realizations of minimally rigid graphs. / Grasegger, Georg.
2025.
DOI RIS ENW BIB
Pentagonal bipyramids lead to the smallest flexible embedded polyhedron
Pentagonal bipyramids lead to the smallest flexible embedded polyhedron. / Gallet, Matteo; Grasegger, Georg; Legerský, Jan et al.
2024.
DOI RIS ENW BIB
Constructing reflection-symmetric flexible realisations of graphs
Constructing reflection-symmetric flexible realisations of graphs. / Dewar, Sean; Grasegger, Georg; Legerský, Jan.
2024.
DOI RIS ENW BIB
Single-cell 3D genome reconstruction in the haploid setting using rigidity theory
Single-cell 3D genome reconstruction in the haploid setting using rigidity theory. / Dewar, Sean; Grasegger, Georg; Kubjas, Kaie et al.
2024.
DOI Download RIS ENW BIB
Angular constraints on planar frameworks
Angular constraints on planar frameworks. / Dewar, Sean; Grasegger, Georg; Nixon, Anthony et al.
2024.
DOI Download RIS ENW BIB
Rigidity of nearly planar classes of graphs
Rigidity of nearly planar classes of graphs. / Dewar, Sean; Grasegger, Georg; Kastis, Eleftherios et al.
2024.
DOI Download RIS ENW BIB
Rigidity of nearly planar classes of graphs
Rigidity of nearly planar classes of graphs. / Dewar, Sean; Grasegger, Georg; Kastis, Eleftherios et al.
2024.
Download RIS ENW BIB
The number of realisations of a rigid graph in Euclidean and spherical geometries
The number of realisations of a rigid graph in Euclidean and spherical geometries. / Dewar, Sean; Grasegger, Georg.
2023.
DOI RIS ENW BIB
Calligraphs and sphere realizations
Calligraphs and sphere realizations. / Gallet, Matteo; Grasegger, Georg; Lubbes, Niels et al.
2023.
DOI RIS ENW BIB
On the uniqueness of collections of pennies and marbles
On the uniqueness of collections of pennies and marbles. / Dewar, Sean; Grasegger, Georg; Kubjas, Kaie et al.
2023.
DOI RIS ENW BIB
Flexibility and rigidity of frameworks consisting of triangles and parallelograms
Flexibility and rigidity of frameworks consisting of triangles and parallelograms. / Grasegger, Georg; Legerský, Jan.
2023.
DOI RIS ENW BIB
Minimal counterexamples to Hendrickson's conjecture on globally rigid graphs
Minimal counterexamples to Hendrickson's conjecture on globally rigid graphs. / Grasegger, Georg.
2022.
DOI RIS ENW BIB
Graph rigidity properties of Ramanujan graphs
Graph rigidity properties of Ramanujan graphs. / Cioabă, Sebastian M; Dewar, Sean; Grasegger, Georg et al.
2022.
DOI Download RIS ENW BIB
Coupler curves of moving graphs and counting realizations of rigid graphs
Coupler curves of moving graphs and counting realizations of rigid graphs. / Grasegger, Georg; Hilany, El; Lubbes, Niels.
2022.
DOI Download RIS ENW BIB
Quotient graphs of symmetrically rigid frameworks
Quotient graphs of symmetrically rigid frameworks. / Dewar, Sean; Grasegger, Georg; Kastis, Eleftherios et al.
2022.
DOI Download RIS ENW BIB
Zero-sum cycles in flexible non-triangular polyhedra
Zero-sum cycles in flexible non-triangular polyhedra. / Gallet, Matteo; Grasegger, Georg; Legerský, Jan et al.
2021.
Download RIS ENW BIB
Zero-sum cycles in flexible polyhedra
Zero-sum cycles in flexible polyhedra. / Gallet, Matteo; Grasegger, Georg; Legerský, Jan et al.
2020.
Download RIS ENW BIB
Bracing frameworks consisting of parallelograms
Bracing frameworks consisting of parallelograms. / Grasegger, Georg; Legerský, Jan.
2020.
Download RIS ENW BIB
Combinatorics of Bricard's octahedra
Combinatorics of Bricard's octahedra. / Gallet, Matteo; Grasegger, Georg; Legerský, Jan et al.
2020.
Download RIS ENW BIB
FlexRiLoG -- A SageMath Package for Motions of Graphs
FlexRiLoG -- A SageMath Package for Motions of Graphs. / Grasegger, Georg; Legerský, Jan.
2020.
Download RIS ENW BIB
On the Classification of Motions of Paradoxically Movable Graphs
On the Classification of Motions of Paradoxically Movable Graphs. / Grasegger, Georg; Legerský, Jan; Schicho, Josef.
2020.
Download RIS ENW BIB
Flexible placements of graphs with rotational symmetry
Flexible placements of graphs with rotational symmetry. / Dewar, Sean; Grasegger, Georg; Legerský, Jan.
2020.
Download RIS ENW BIB
Flexible circuits in the d-dimensional rigidity matroid
Flexible circuits in the d-dimensional rigidity matroid. / Grasegger, Georg; Guler, Hakan; Jackson, Bill et al.
2020.
Download RIS ENW BIB
Classification of motions of the 3-connected Harary graph on 7 vertices
Classification of motions of the 3-connected Harary graph on 7 vertices. / Grasegger, Georg; Legerský, Jan; Schicho, Josef.
2019. 17 S.
DOI RIS ENW BIB
On the existence of paradoxical motions of generically rigid graphs on the sphere
On the existence of paradoxical motions of generically rigid graphs on the sphere. / Gallet, Matteo; Grasegger, Georg; Legerský, Jan et al.
2019.
Download RIS ENW BIB
Counting realizations of Laman graphs on the sphere
Counting realizations of Laman graphs on the sphere. / Gallet, Matteo; Grasegger, Georg; Schicho, Josef.
2019.
Download RIS ENW BIB
Graphs with Flexible Labelings allowing Injective Realizations
Graphs with Flexible Labelings allowing Injective Realizations. / Grasegger, Georg; Legerský, Jan; Schicho, Josef.
2018.
Download RIS ENW BIB
Lower bounds on the number of realizations of rigid graphs
Lower bounds on the number of realizations of rigid graphs. / Grasegger, Georg; Koutschan, Christoph; Tsigaridas, Elias.
Linz, 2017. 22 S.
Download RIS ENW BIB
Graphs with Flexible Labelings
Graphs with Flexible Labelings. / Grasegger, Georg; Legersky, Jan; Schicho, Josef.
2017.
Download RIS ENW BIB
The number of realizations of a Laman graph
The number of realizations of a Laman graph. / Capco, Jose; Gallet, Matteo; Grasegger, Georg et al.
Linz, 2017. 42 S.
Download RIS ENW BIB
An Algebraic-Geometric Method for Computing Zolotarev Polynomials — Additional Information
An Algebraic-Geometric Method for Computing Zolotarev Polynomials — Additional Information. / Grasegger, Georg.
2016.
Website RIS ENW BIB
An Algebraic-Geometric Method for Computing Zolotarev Polynomials
An Algebraic-Geometric Method for Computing Zolotarev Polynomials. / Grasegger, Georg; Vo, Thieu N.
2016.
Website RIS ENW BIB
Statistical Investigation of First-Order Algebraic ODEs and their Rational General Solutions
Statistical Investigation of First-Order Algebraic ODEs and their Rational General Solutions. / Grasegger, Georg; Vo, Thieu N; Winkler, Franz.
2015.
Website RIS ENW BIB

Dataset of realisation numbers of rigid graphs in dimension 2
Dataset of realisation numbers of rigid graphs in dimension 2
Dewar, S., Grasegger, G., Schicho, J., Tewari, A. K. & Warren, A., Austrian Academy of Sciences, 17 Sep. 2025
DOI: 10.5281/zenodo.17144281
Non-planar graphs with various apex properties
Non-planar graphs with various apex properties
Grasegger, G., Dewar, S., Kastis, E., Nixon, A. & Servatius, B., Austrian Academy of Sciences, 2024
DOI: 10.5281/zenodo.10671129, https://doi.org/10.5281/zenodo.10671129
Non-planar apex graphs with different independence properties
Non-planar apex graphs with different independence properties
Grasegger, G., Dewar, S., Kastis, E., Nixon, A. & Servatius, B., Austrian Academy of Sciences, 2024
DOI: 10.5281/zenodo.10671321, https://doi.org/10.5281/zenodo.10671321
Non-planar (3,6)-sparse graphs with various apex properties
Non-planar (3,6)-sparse graphs with various apex properties
Grasegger, G., Dewar, S., Kastis, E., Nixon, A. & Servatius, B., Austrian Academy of Sciences, 2024
DOI: 10.5281/zenodo.10671293, https://doi.org/10.5281/zenodo.10671293
Dataset of (3,6)-tight graphs
Dataset of (3,6)-tight graphs
Grasegger, G., Austrian Academy of Sciences, 2024
DOI: 10.5281/zenodo.13768206, https://doi.org/10.5281/zenodo.13768206
Circuits in the 3-dimensional rigidity matroid
Circuits in the 3-dimensional rigidity matroid
Grasegger, G., Austrian Academy of Sciences, 2024
DOI: 10.5281/zenodo.10671346, https://doi.org/10.5281/zenodo.10671346
Marble graphs with various rigidity properties
Marble graphs with various rigidity properties
Dewar, S., Grasegger, G., Kubjas, K., Mohammadi, F. & Nixon, A., Austrian Academy of Sciences, 2023
DOI: 10.5281/zenodo.8114282, https://doi.org/10.5281/zenodo.8114282
Dataset of redundantly rigid graphs
Dataset of redundantly rigid graphs
Grasegger, G., Austrian Academy of Sciences, 2022
DOI: 10.5281/zenodo.7473079, https://doi.org/10.5281/zenodo.7473079
Dataset of globally rigid graphs
Dataset of globally rigid graphs
Grasegger, G., Austrian Academy of Sciences, 2022
DOI: 10.5281/zenodo.7473053, https://doi.org/10.5281/zenodo.7473053
Ramanujan graphs with degree 3, 4, 5, 6, or 7
Ramanujan graphs with degree 3, 4, 5, 6, or 7
M Cioabă, S., Dewar, S., Grasegger, G. & Gu, X., Austrian Academy of Sciences, 2022
DOI: 10.5281/zenodo.6579837, https://doi.org/10.5281/zenodo.6579837
Rigidity of 4-regular Ramanujan graphs
Rigidity of 4-regular Ramanujan graphs
M Cioabă, S., Dewar, S., Grasegger, G. & Gu, X., Austrian Academy of Sciences, 2022
DOI: 10.5281/zenodo.6579718, https://doi.org/10.5281/zenodo.6579718
The number of realizations of all Laman graphs with at most 12 vertices
The number of realizations of all Laman graphs with at most 12 vertices
Capco, J., Gallet, M., Grasegger, G., Koutschan, C., Lubbes, N. & Schicho, J., Austrian Academy of Sciences, 2018
DOI: 10.5281/zenodo.1245517, https://doi.org/10.5281/zenodo.1245517

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Name	Purpose	Storage duration	Type	Provider
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People

Georg Grasegger

Georg Grasegger

Research interests

Publications

Dataset of realisation numbers of rigid graphs in dimension 2

Non-planar graphs with various apex properties

Non-planar apex graphs with different independence properties

Non-planar (3,6)-sparse graphs with various apex properties

Dataset of (3,6)-tight graphs

Circuits in the 3-dimensional rigidity matroid

Marble graphs with various rigidity properties

Dataset of redundantly rigid graphs

Dataset of globally rigid graphs

Ramanujan graphs with degree 3, 4, 5, 6, or 7

Rigidity of 4-regular Ramanujan graphs

The number of realizations of all Laman graphs with at most 12 vertices