Research
Interests
I am interested in various branches of discrete mathematics and computer science. Below, some of the main directions of my research work so far are listed:- chromatic graph theory: mostly different types of edge-colorings (strong, star, acyclic), non-classical vertex colorings (injective, types of facial), incidence colorings, etc;
- properties of complex networks: analysis and determination of substructures (communities, core-periphery) in networks for faster recognition of relevant properties;
- analysis of real complex networks: mostly collaboration networks;
-
combinatorics on words:
properties of Thue sequences,
(k+2) -conjecture fork -Thue sequences. - chemical graph theory: structural properties of fullerene graphs, topological indices (extremal values and graphs achieving them);
Conference talks
- Combining proper and square colorings , 31st Workshop Cycles and Colourings, High Tatras, Slovakia (2023).
- Coloring edges of subcubic graphs with five colors, 4th Croatian Combinatorial Days, Zagreb, Croatia (2022).
- Coloring vertices with neighborhood constraints Maribor Graph Theory Conference, Maribor, Slovenia (2022).
- Coloring vertices with neighborhood constraints , 30th Workshop Cycles and Colourings, High Tatras, Slovakia (2022).
- Edge-coloring subcubic graphs with five colors [Zoom lecture], China-Slovenia: Symposium on Modern Graph Theory, Online (2021).
- Edge-coloring subcubic graphs with five colors [Zoom lecture], Online Workshop on Applied Mathematics, Ostrava, Czech Republic (2021).
- Edge-coloring (sub)cubic graphs with 5 colors [Zoom lecture], 5th Macedonian Workshop on Graph Theory and Applied Mathematics, Ohrid, North Macedonia (2021).
- Edge-coloring (sub)cubic graphs with 5 colors , 29th Workshop Cycles and Colourings, High Tatras, Slovakia (2021).
- Open problems in S-packing edge-coloring, Workshop on Embedded Graphs - Colorings and Structure, Jablonov nad Turňou, Slovakia (2021). [ pdf ]
- Cubic graphs, edge-colorings and 5 colors, 3rd Workshop on Graph Colorings, Herl'any, Slovakia (2020).
- Homogeneous coloring of vertices, 28th '3in1' Workshop, Dosłońce, Poland (2019).
- Between proper and strong edge-colorings of subcubic graphs [invited talk], 28th Workshop Cycles and Colourings, High Tatras, Slovakia (2019).
- Homogeneous Coloring of Graphs, 9th Slovenian International Conference on Graph Theory - Bled'19, Bled, Slovenia (2019). [ pdf ]
- Repetition Thresholds in Graphs, The 54rd Czech-Slovak Conference Graphs 2019, Čingov, Slovakia (2019). [ pdf ]
- On 3-choosability of planar graphs with maximum degree 4, 8th Cracow Conference on Graph Theory "Rytro '18", Rytro, Poland (2018). [ pdf ]
- On 3-choosability of planar graphs with maximum degree 4, 27th Workshop Cycles and Colourings, High Tatras, Slovakia (2018).
- On vertex-parity edge-coloring , The 6th Gdansk Workshop on Graph Theory, Gdansk, Poland (2018).
- Star Edge-Coloring [invited talk], The 53rd Czech-Slovak Conference Graphs 2018, Prague, Czech Republic (2018). [ pdf ]
- Colorful Graph Theory [invited talk], 19. Konferencia košických matematikov, Herl'any, Slovakia (2018). [ pdf ]
- Edge-colorings as edge-decompositions, Ljubljana - Leoben Graph Theory Seminar 2017, Maribor, Slovenia (2017).
- Edge-colorings as edge-decompositions, Workshop Cycles and Colourings, High Tatras, Slovakia (2017). [ pdf ]
- Results on locally irregular edge-coloring, The 52nd Czech-Slovak Conference on Combinatorics and Graph Theory, Hejnice, Czech Republic (2017). [ pdf ]
- Edge-coloring Variations [invited talk], II Studencka Konferencja KNDM, Krakow, Poland (2017). [ pdf ]
- Edge-colorings: Results & Problems, Workshop on Graph Colourings, Plzeň, Czech Republic (2017). [ Prezi ]
- Locally irregular edge-coloring & related topics, 25th Workshop '3in1', Dosłońce, Poland (2016). [ pdf ]
- On incidence colorings of graphs, 1st Croatian Combinatorial Days, Zagreb, Croatia (2016). [ pdf ]
- Incidence coloring: The (Δ+2)-conjecture, Workshop Cycles and Colourings, High Tatras, Slovakia (2016). [ pdf ]
- On injective colorings of graphs (a survey), Workshop Cycles and Colourings, Novy Smokovec, Slovakia (2014). [ pdf ]
- The Way to efficient management of complex engineering design, ITIS - 5th International Conference on Information Technologies and Information Society, Dolenjske Toplice, Slovenia (2013).
- Interdisciplinarity of Slovenian research, ITIS - 5th International Conference on Information Technologies and Information Society, Dolenjske Toplice, Slovenia (2013). [ pdf ]
- On facial parity edge colorings, Seventh Czech-Slovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications, Košice, Slovakia (2013). [ pdf ]
2023
2022
2021
2020
2019
2018
2017
2016
2014
2013
Seminar talks
- Combining Proper and Square Colorings, Graphs & Optimization Seminar, University of Bordeaux, Talence, France (September, 2023).
- Combining Proper and Square Colorings, Seminarium KTGiZU, Warsaw University of Technology, Poland (April, 2023).
- Coloring Vertices with Neighborhood Constraints, Košický kombinatorický seminár, Košice, Slovakia (2022).
- From proper to strong edge-colorings of (sub)cubic graphs, ISU Discrete Mathematics Zoominar, Iowa, USA (2021).
- Between proper and strong edge-colorings, Graph Theory Seminar, University of West Bohemia, Pilsen, Czech Republic (2019).
- Between proper and strong edge-colorings, Mathematical Research Seminar, University of Primorska, Koper, Slovenia (2019).
- IPE - The Extensible Drawing Editor by Otfried Cheong, Košický kombinatorický seminár, Košice, Slovakia (2019). [ pdf ]
- Star edge-coloring, Graphs & Optimization Seminar, University of Bordeaux, Talence, France (2019). [ pdf ]
- Some coloring properties of medial graphs, Košický kombinatorický seminár, Košice, Slovakia (2018). [ pdf ]
- 3-choosability of planar graphs with maximum degree 4, Graph Theory Seminar, University of West Bohemia, Pilsen, Czech Republic (2018). [ pdf ]
- Repetition Thresholds in Graphs, Košický kombinatorický seminár, Košice, Slovakia (2018). [ pdf ]
- The (Δ+2)-conjecture in incidence colorings of graphs, Discrete Mathematics Seminar, AGH University of Science and Technology, Krakow, Poland (2016). [ pdf ]
- The (Δ+2)-conjecture in incidence colorings of graphs, Graph Theory Seminar, University of West Bohemia, Pilsen, Czech Republic (2016).
- On Incidence Colorings of Graphs, Seminar iz diskretne matematike, Maribor, Slovenia (2016). [ pdf ]
- On Packing Colorings (of Hypercubes), Košický kombinatorický seminár, Košice, Slovakia (2015).
- Incidence colorings of Cartesian products, Košický kombinatorický seminár, Košice, Slovakia (2015).
2023
2022
2021
2019
2018
2016
2015
Coworkers
During my research work I had an honor and opportunity to work with many great scientists and extraordinary people. Listed are only coauthors of published papers or papers in preparation (in alphabetical order):- Vesna Andova, Stéphane Bessy, Drago Bokal, Marthe Bonamy, Brankica Bratić, Marek Cygan, Darko Dimitrov, Tomislav Došlić, François Dross, Igor Fabrici, Jiři Fink, Tanja Gologranc, Petr Gregor, Ivan Gutman, Herve Hocquard, David Hudák, Maria Janicová, František Kardoš, Mario Karlovčec, Andrej Kastrin, Jelena Klisara, Martin Knor, Łukasz Kowalik, Daniel Kraĺ, Matjaž Krnc, Jaka Kranjc, Martin Kupec, Hoang La, Dimitri Lajou, Zoran Levnajić, Bernard Lidický, Mária Maceková, Tomaš Madaras, Luka Mali, Dunja Mladenić, Martina Mockovčiaková, Dolores Modic, Pascal Ochem, Alenka Pandiloska Jurak, Matjaž Perc, Mirko Petruševski, Alexandre Pinlou, Janez Povh, Jakub Przybyło, Edo Ravnikar, Martin Ravnikar, Simona Rindošová, Katarina Rojko, Roman Soták, Ľudmila Šebestová, Riste Škrekovski, Roman Šoper, Katarina Sroková, Peter Šugerek, Martin Tancer, Jan Volec, Tohru Yoshioka-Kobayashi.
Useful links
- House of graphs : a database of interesting (small order) graphs;
- Open problem garden : a collection of unsolved problems in mathematics;
- The On-line Encyclopedia of Integer Sequences
- Highcharts : interactive charts based on javascript;
- Overleaf : online latex editor.
- Garfield : regular fun.