About Me

I have a PhD degree in algebra and number theory. My teaching spans several fields of abstract algebra, discrete mathematics, and theoretical computer science.

As concerns my research activities, I am interested in problems related to symmetries of discrete objects, problems related to the structure of snarks, and some other problems of classical graph theory.

Actual positions

• Associate professor, Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Information Sciences, Slovak University of Technology
• Researcher (part-time), Mathematical Institute of Slovak Academy of Sciences

Qualification and degrees

• Associate professor of mathematics (2015) Matej Bel University in Banská Bystrica. Thesis: Discrete Group Actions: Algorithms and Applications
• Philosophiae doctor (2006) Mathematical Institute of Slovak Academy of Sciences, Bratislava, in the field "Algebra and Number Theory". Thesis: 3-Manifolds with Heegaard Genus at most Two.

Publications

• Karabáš, J., Máčajová, E., Nedela, R., Škoviera, M. Colouring defect of a cubic graph and the conjectures of Fan-Raspaud and Fulkerson, Ars Mathematica Contemporanea 26 No. 2 (2026) #P2.02, https://doi.org/10.26493/1855-3974.3291.a20 (also arXiv:2312.13638 [math.CO], (v1) 21 Dec 2023).
• Karabáš, J., Máčajová, E., Nedela, R., Škoviera, M. Colouring defect of strong snarks, Procedia Computer Science 273, 2025, Pages 149-155.
• Karabáš, J., Máčajová, E., Nedela, R., Škoviera, M. Short cycle covers and the colouring defect of a cubic graph, Procedia Computer Science 273, 2025, Pages, 2025, 156–162.
• Karabáš, J., Máčajová, E., Nedela, R., Škoviera, M. Cubic graphs of colouring defect 3 and conjectures of Berge and Alon-Tarsi, arXiv:2505.17569 [math.CO], (v1) 23 May 2025.
• Karabáš, J., Máčajová, E., Nedela, R., Škoviera, M. Berge's conjecture for cubic graphs with small colouring defect, Journal of Graph Theory 109, Issue 3, March 2025, 387-396 (also arXiv:2210.13234 [math.CO], (v3) 9 Jan 2025).
• Estélyi, I., Karabáš, J., Mednykh, A., Nedela, R. The Jacobian of a graph and graph automorphisms, Discrete Mathematics 348, Issue 2, February 2025, 114259. (also arXiv:2206.01469 [math.CO]).
• Karabáš, J., Máčajová, E., Nedela, R., Škoviera, M. Cubic graphs with colouring defect 3, Electronic Journal of Combinatorics 31, Issue 2, Apr 5 2024, P26. (also arXiv:2308.13639 [math.CO]).
• Karabáš, J., Nedela, R., Skyvová, M. Computing equivalence classes of finite group actions on orientable surfaces, J. Pure Appl. Algebra, 228 Issue 6 (2024), 107578. (also arXiv:2203.05812 [math.GR]).
• Karabáš, J., Máčajová, E., Nedela, R., Škoviera, M. Perfect-matching covers of cubic graphs with colouring defect 3, In: Proceedings of EUROCOMB'23, MUNI Press, 639–646.
• Karabáš, J., Máčajová, E., Nedela, R., Škoviera, M. Girth, oddness, and colouring defect of snarks, Discrete Mathematics 345, Issue 11, December 2022, 113040 (also arXiv:2106.12205 [math.CO])
• Estélyi, I., Karabáš, J., Mednykh, A., Nedela, R. On a representation of the automorphism group of a graph in a unimodular group, Discrete Mathematics 344, Issue 12, December 2021, 112606. (also arXiv:2102.04239 [math.CO]).
• d’Azevedo, A.B., Catalano, D.A., Karabáš, J., Nedela, R. Quadrangle Group Inclusions, Beitr. Algebra Geom. (2017) 58, pp. 369-394.
• d’Azevedo A.B., Catalano D.A., Karabáš J., Nedela R. Census of Quadrangle Groups Inclusions. In: Širáň J., Jajcay R. (eds) Symmetries in Graphs, Maps, and Polytopes. SIGMAP 2014. Springer Proceedings in Mathematics & Statistics, vol 159. Springer, Cham.
• d'Azevedo, A. B., Catalano, D. A., and Karabáš, J., Two infinite families of Archimedean maps of higher genera , Ars Combinatoria 128, pp. 241-254, 2016.
• d'Azevedo, A. B., Catalano, D. A., Karabáš, J., and Nedela, R., Maps of Archimedean Class and operations on dessins, Discrete Mathematics 338, Issue 10, (2015), 1814–1825, Proceedings of the Seventh Czech-Slovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications, Košice 2013.
• Karabáš, J., Máčajová, E., and Nedela, R., 6-decomposition of snarks, European Journal of Combinatorics 34 (2013), 111 - 122
• Karabáš, J., and Nedela, R., Archimedean maps of higher genera, Math. Comp. 81 (2012), 569-583.
• Karabáš, J., and Nedela, R., Archimedean solids of genus two, Electronic Notes in Discrete Mathematics 28 (2007), 331-339.
• Karabáš, J., Maličký, P., and Nedela, R., Three-manifolds with Heegaard genus at most two represented by crystallisations with at most 42 vertices , Discrete Mathematics 307 (2007), 2569 - 2590.
• Karabáš, J., Maličký, P., and Nedela, R., Fundamental groups of prime 3-manifolds of genus at most two , Tatra Mountains Math. Publ. 36 (2007), 1-11, Proceedings of conference "Graphs 2004".
• Karabáš, J., and Nedela, R., Minimal Representatives of G-classes of 3-Manifolds of Genus Two, Acta Univ. M. Belii. Ser. Mathematics 10 (2003), 21-42.