Computational Mathematics

📝 Publications and preprints

Preprints

1. Mundinger, K., Zimmer, M., Kiem, A., Spiegel, C., and Pokutta, S. (2025). Neural Discovery in Mathematics: Do Machines Dream of Colored Planes? [arXiv]
   [BibTeX]

   @misc{2025_MundingerZimmerKiemSpiegelPokutta_NeuralDiscovery,
     archiveprefix = {arXiv},
     eprint = {2501.18527},
     primaryclass = {cs.LG},
     year = {2025},
     author = {Mundinger, Konrad and Zimmer, Max and Kiem, Aldo and Spiegel, Christoph and Pokutta, Sebastian},
     title = {Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?},
     date = {2025-01-30}
   }

2. Espuny Díaz, A., Gupta, P., Mergoni Cecchelli, D., Parczyk, O., and Sgueglia, A. (2024). Dirac’s Theorem for Graphs of Bounded Bandwidth. [arXiv]
   [BibTeX]

   @misc{2024_AlbertoEtAl_Diractheorembandwidth,
     archiveprefix = {arXiv},
     eprint = {2407.05889},
     primaryclass = {math.CO},
     year = {2024},
     author = {Espuny Díaz, Alberto and Gupta, Pranshu and Mergoni Cecchelli, Domenico and Parczyk, Olaf and Sgueglia, Amédeo},
     title = {Dirac's Theorem for Graphs of Bounded Bandwidth},
     date = {2024-07-08}
   }

3. Illingworth, F., Lang, R., Müyesser, A., Parczyk, O., and Sgueglia, A. (2024). Spanning Spheres in Dirac Hypergraphs. [arXiv]
   [BibTeX]

   @misc{2024_FreddieEtAl_Spanningspheresdirac,
     archiveprefix = {arXiv},
     eprint = {2407.06275},
     primaryclass = {math.CO},
     year = {2024},
     author = {Illingworth, Freddie and Lang, Richard and Müyesser, Alp and Parczyk, Olaf and Sgueglia, Amédeo},
     title = {Spanning Spheres in Dirac Hypergraphs},
     date = {2024-07-08}
   }

4. Kiem, A., Parczyk, O., and Spiegel, C. (2024). Forcing Graphs to Be Forcing. [arXiv]
   [BibTeX]

   @misc{2024_KiemParczykSpiegel_Forcing,
     archiveprefix = {arXiv},
     eprint = {2412.12904},
     primaryclass = {math.CO},
     year = {2024},
     author = {Kiem, Aldo and Parczyk, Olaf and Spiegel, Christoph},
     title = {Forcing Graphs to Be Forcing},
     date = {2024-12-17}
   }

5. Parczyk, O., and Spiegel, C. (2024). An Unsure Note on an Un-Schur Problem. [arXiv]
   [BibTeX]

   @misc{2024_ParczykSpiegel_UnSchur,
     archiveprefix = {arXiv},
     eprint = {2410.22024},
     primaryclass = {math.CO},
     year = {2024},
     author = {Parczyk, Olaf and Spiegel, Christoph},
     title = {An Unsure Note on an Un-Schur Problem},
     date = {2024-10-29}
   }

6. Böttcher, J., Frankl, N., Mergoni Cecchelli, D., Skokan, J., and Parczyk, O. (2023). Graphs with Large Minimum Degree and No Small Odd Cycles Are 3-colourable. [arXiv]
   [BibTeX]

   @misc{2023_BoettcherEtAl_Graphs3colourable,
     archiveprefix = {arXiv},
     eprint = {2302.01875},
     primaryclass = {math.CO},
     year = {2023},
     author = {Böttcher, Julia and Frankl, Nóra and Mergoni Cecchelli, Domenico and Skokan, Jozef and Parczyk, Olaf},
     title = {Graphs with Large Minimum Degree and No Small Odd Cycles Are 3-colourable},
     date = {2023-02-03}
   }

7. Mattos, L., Mergoni Cecchelli, D., and Parczyk, O. (2023). On Product Schur Triples in the Integers. [arXiv]
   [BibTeX]

   @misc{2023_MattosDomenicoParczyk_Productschurtriples,
     archiveprefix = {arXiv},
     eprint = {2311.18796},
     primaryclass = {math.CO},
     year = {2023},
     author = {Mattos, Letícia and Mergoni Cecchelli, Domenico and Parczyk, Olaf},
     title = {On Product Schur Triples in the Integers},
     date = {2023-11-30}
   }

8. Braun, G., Pokutta, S., and Weismantel, R. (2022). Alternating Linear Minimization: Revisiting von Neumann’s Alternating Projections. [arXiv] [slides] [video]
   [BibTeX]

   @misc{2022_BraunPokuttaWeismantel_Alternatingminimization,
     archiveprefix = {arXiv},
     eprint = {2212.02933},
     primaryclass = {math.OC},
     year = {2022},
     author = {Braun, Gábor and Pokutta, Sebastian and Weismantel, Robert},
     title = {Alternating Linear Minimization: Revisiting von Neumann's Alternating Projections},
     slides = {https://pokutta.com/slides/20230327-icerm.pdf},
     video = {https://icerm.brown.edu/programs/sp-s23/w2/#schedule-item-4945},
     date = {2022-12-06}
   }

Conference proceedings

1. Kiem, A., Pokutta, S., and Spiegel, C. (2024). The Four-color Ramsey Multiplicity of Triangles. Proceedings of the Discrete Mathematics Days. [URL] [arXiv] [code]
   [BibTeX]

   @inproceedings{2023_KiemPokuttaSpiegel_4colorramsey,
     year = {2024},
     booktitle = {Proceedings of the Discrete Mathematics Days},
     url = {https://dmd2024.web.uah.es/files/abstracts/paper_3.pdf},
     archiveprefix = {arXiv},
     eprint = {2312.08049},
     primaryclass = {math.CO},
     author = {Kiem, Aldo and Pokutta, Sebastian and Spiegel, Christoph},
     title = {The Four-color Ramsey Multiplicity of Triangles},
     code = {https://github.com/FordUniver/kps_trianglemult}
   }

2. Kiem, A., Pokutta, S., and Spiegel, C. (2024). Categorification of Flag Algebras. Proceedings of the Discrete Mathematics Days. [URL]
   [BibTeX]

   @inproceedings{2024_KiemPokuttaSpiegel_Categorificationflagalgebras,
     year = {2024},
     booktitle = {Proceedings of the Discrete Mathematics Days},
     url = {https://dmd2024.web.uah.es/files/abstracts/paper_47.pdf},
     author = {Kiem, Aldo and Pokutta, Sebastian and Spiegel, Christoph},
     title = {Categorification of Flag Algebras}
   }

3. Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024, April 8). Extending the Continuum of Six-Colorings. Proceedings of the Discrete Mathematics Days. [URL] [arXiv]
   [BibTeX]

   @inproceedings{2024_MundingerPokuttaSpiegelZimmer_SixcoloringsExpansion:1,
     year = {2024},
     booktitle = {Proceedings of the Discrete Mathematics Days},
     url = {https://dmd2024.web.uah.es/files/abstracts/paper_27.pdf},
     archiveprefix = {arXiv},
     eprint = {2404.05509},
     primaryclass = {math.CO},
     author = {Mundinger, Konrad and Pokutta, Sebastian and Spiegel, Christoph and Zimmer, Max},
     title = {Extending the Continuum of Six-Colorings},
     date = {2024-04-08}
   }

4. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2023). Fully Computer-assisted Proofs in Extremal Combinatorics. Proceedings of the AAAI Conference on Artificial Intelligence. DOI: 10.1609/aaai.v37i10.26470 [URL] [arXiv] [code]
   [BibTeX]

   @inproceedings{2022_ParczykPokuttaSpiegelSzabo_Ramseymultiplicityheuristics:1,
     year = {2023},
     booktitle = {Proceedings of the AAAI Conference on Artificial Intelligence},
     doi = {10.1609/aaai.v37i10.26470},
     url = {https://ojs.aaai.org/index.php/AAAI/article/view/26470},
     archiveprefix = {arXiv},
     eprint = {2206.04036},
     primaryclass = {math.CO},
     author = {Parczyk, Olaf and Pokutta, Sebastian and Spiegel, Christoph and Szabó, Tibor},
     title = {Fully Computer-assisted Proofs in Extremal Combinatorics},
     code = {https://zenodo.org/record/6602512#.YyvFhi8Rr5g}
   }

5. Rué, J. J., and Spiegel, C. (2023, April 1). The Rado Multiplicity Problem in Vector Spaces Over Finite Fields. Proceedings of the European Conference on Combinatorics, Graph Theory and Applications. DOI: 10.5817/CZ.MUNI.EUROCOMB23-108 [URL] [arXiv] [code]
   [BibTeX]

   @inproceedings{2023_RueSpiegel_Radomultiplicity,
     year = {2023},
     booktitle = {Proceedings of the European Conference on Combinatorics, Graph Theory and Applications},
     doi = {10.5817/CZ.MUNI.EUROCOMB23-108},
     url = {https://journals.muni.cz/eurocomb/article/view/35642},
     archiveprefix = {arXiv},
     eprint = {2304.00400},
     primaryclass = {math.CO},
     author = {Rué, Juan José and Spiegel, Christoph},
     title = {The Rado Multiplicity Problem in Vector Spaces Over Finite Fields},
     code = {https://github.com/FordUniver/rs_radomult_23},
     date = {2023-04-01}
   }

6. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2022, July 1). New Ramsey Multiplicity Bounds and Search Heuristics. Proceedings of the Discrete Mathematics Days. [arXiv] [code]
   [BibTeX]

   @inproceedings{2022_ParczykPokuttaSpiegelSzabo_Ramseymultiplicityheuristics:2,
     year = {2022},
     date = {2022-07-01},
     booktitle = {Proceedings of the Discrete Mathematics Days},
     archiveprefix = {arXiv},
     eprint = {2206.04036},
     primaryclass = {math.CO},
     author = {Parczyk, Olaf and Pokutta, Sebastian and Spiegel, Christoph and Szabó, Tibor},
     title = {New Ramsey Multiplicity Bounds and Search Heuristics},
     code = {https://zenodo.org/record/6602512#.YyvFhi8Rr5g}
   }

7. Böttcher, J., Sgueglia, A., Skokan, J., and Parczyk, O. (2021). The Square of a Hamilton Cycle in Randomly Perturbed Graphs. Proceedings of the European Conference on Combinatorics, Graph Theory and Applications, 14, 644–650. DOI: 10.1007/978-3-030-83823-2_103 [arXiv]
   [BibTeX]

   @inproceedings{2024_BoettcherAmedeoJozefParczyk_Hamiltoncycleperturbation:1,
     year = {2021},
     booktitle = {Proceedings of the European Conference on Combinatorics, Graph Theory and Applications},
     volume = {14},
     pages = {644-650},
     doi = {10.1007/978-3-030-83823-2_103},
     archiveprefix = {arXiv},
     eprint = {2202.05215},
     primaryclass = {math.CO},
     author = {Böttcher, Julia and Sgueglia, Amédeo and Skokan, Jozef and Parczyk, Olaf},
     title = {The Square of a Hamilton Cycle in Randomly Perturbed Graphs}
   }

8. Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (2017, November 20). Random Strategies Are Nearly Optimal for Generalized Van Der Waerden Games. Proceedings of the European Conference on Combinatorics, Graph Theory and Applications. [URL] [arXiv]
   [BibTeX]

   @inproceedings{2017_KuschRueSpiegelSzabo_Uniformrandomstrategy:1,
     year = {2017},
     booktitle = {Proceedings of the European Conference on Combinatorics, Graph Theory and Applications},
     url = {https://dmg.tuwien.ac.at/eurocomb2017/index.php/accepted-papers/},
     archiveprefix = {arXiv},
     eprint = {1711.07251},
     primaryclass = {math.CO},
     author = {Kusch, Christopher and Rué, Juan José and Spiegel, Christoph and Szabó, Tibor},
     title = {Random Strategies Are Nearly Optimal for Generalized Van Der Waerden Games},
     date = {2017-11-20}
   }

Full articles

1. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2024). New Ramsey Multiplicity Bounds and Search Heuristics. Foundations of Computational Mathematics. DOI: 10.1007/s10208-024-09675-6 [arXiv] [code]
   [BibTeX]

   @article{2022_ParczykPokuttaSpiegelSzabo_Ramseymultiplicityheuristics,
     year = {2024},
     journal = {Foundations of Computational Mathematics},
     date = {2024-08-06},
     doi = {10.1007/s10208-024-09675-6},
     archiveprefix = {arXiv},
     eprint = {2206.04036},
     primaryclass = {math.CO},
     author = {Parczyk, Olaf and Pokutta, Sebastian and Spiegel, Christoph and Szabó, Tibor},
     title = {New Ramsey Multiplicity Bounds and Search Heuristics},
     code = {https://zenodo.org/record/6602512#.YyvFhi8Rr5g}
   }

2. Böttcher, J., Sgueglia, A., Skokan, J., and Parczyk, O. (2024). The Square of a Hamilton Cycle in Randomly Perturbed Graphs. Random Structures & Algorithms, 65(2), 342–368. DOI: 10.1002/rsa.21215 [arXiv]
   [BibTeX]

   @article{2024_BoettcherAmedeoJozefParczyk_Hamiltoncycleperturbation,
     year = {2024},
     journal = {Random Structures & Algorithms},
     volume = {65},
     number = {2},
     pages = {342-368},
     doi = {10.1002/rsa.21215},
     archiveprefix = {arXiv},
     eprint = {2202.05215},
     primaryclass = {math.CO},
     author = {Böttcher, Julia and Sgueglia, Amédeo and Skokan, Jozef and Parczyk, Olaf},
     title = {The Square of a Hamilton Cycle in Randomly Perturbed Graphs}
   }

3. Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024). Extending the Continuum of Six-Colorings. Geombinatorics Quarterly, XXXIV. [URL] [arXiv]
   [BibTeX]

   @article{2024_MundingerPokuttaSpiegelZimmer_SixcoloringsExpansion,
     year = {2024},
     journal = {Geombinatorics Quarterly},
     date = {2024-07-01},
     volume = {XXXIV},
     url = {https://geombina.uccs.edu/past-issues/volume-xxxiv},
     archiveprefix = {arXiv},
     eprint = {2404.05509},
     primaryclass = {math.CO},
     author = {Mundinger, Konrad and Pokutta, Sebastian and Spiegel, Christoph and Zimmer, Max},
     title = {Extending the Continuum of Six-Colorings}
   }

4. Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (2018). On the Optimality of the Uniform Random Strategy. Random Structures & Algorithms, 55(2), 371–401. DOI: 10.1002/rsa.20829 [URL] [arXiv]
   [BibTeX]

   @article{2017_KuschRueSpiegelSzabo_Uniformrandomstrategy,
     year = {2019-09},
     journal = {Random Structures & Algorithms},
     date = {2018-12-10},
     volume = {55},
     number = {2},
     pages = {371-401},
     doi = {10.1002/rsa.20829},
     url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/rsa.20829},
     archiveprefix = {arXiv},
     eprint = {1711.07251},
     primaryclass = {math.CO},
     author = {Kusch, Christopher and Rué, Juan José and Spiegel, Christoph and Szabó, Tibor},
     title = {On the Optimality of the Uniform Random Strategy}
   }