Computational Mathematics

📝 Publications and preprints

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},
     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. 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}
   }

3. Díaz, A. E., Gupta, P., Cecchelli, D. M., 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 = {Díaz, Alberto Espuny and Gupta, Pranshu and Cecchelli, Domenico Mergoni and Parczyk, Olaf and Sgueglia, Amédeo},
     title = {Dirac's Theorem for Graphs of Bounded Bandwidth}
   }

4. 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}
   }

5. 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}
   }

6. 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}
   }

7. 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},
     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}
   }

8. Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024). 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}
   }

9. 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}
   }

10. 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}
    }

11. Böttcher, J., Frankl, N., Cecchelli, D. M., 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 Cecchelli, Domenico Mergoni and Skokan, Jozef and Parczyk, Olaf},
      title = {Graphs with Large Minimum Degree and No Small Odd Cycles Are 3-colourable}
    }

12. Mattos, L., Cecchelli, D. M., 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 Cecchelli, Domenico Mergoni and Parczyk, Olaf},
      title = {On Product Schur Triples in the Integers}
    }

13. Rué, J. J., and Spiegel, C. (2023). 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}
    }

14. 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}
    }

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

    @inproceedings{2022_ParczykPokuttaSpiegelSzabo_Ramseymultiplicityheuristics:2,
      year = {2022},
      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}
    }

16. Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (2019-09). 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},
      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 = {2411.02622},
      primaryclass = {cs.LG},
      author = {Kusch, Christopher and Rué, Juan José and Spiegel, Christoph and Szabó, Tibor},
      title = {On the Optimality of the Uniform Random Strategy}
    }

17. Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (2017). 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 = {2411.02622},
      primaryclass = {cs.LG},
      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}
    }