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 edgecolorings (strong, star, acyclic), nonclassical vertex colorings (injective, types of facial),
incidence colorings, etc;

properties of complex networks:
analysis and determination of substructures (communities, coreperiphery) 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 for kThue sequences.

chemical graph theory:
structural properties of fullerene graphs, topological indices (extremal values and graphs achieving them);
Conference talks

On 3choosability of planar graphs with maximum degree 4,
8th Cracow Conference on Graph Theory "Rytro '18", Rytro, Poland (2018).
[ pdf ]

On 3choosability of planar graphs with maximum degree 4,
Cycles and Colourings, High Tatras, Slovakia (2018).

On vertexparity edgecoloring ,
The 6th Gdansk Workshop on Graph Theory, Gdansk, Poland (2018).

Star EdgeColoring [invited talk],
The 53rd CzechSlovak Conference Graphs 2018, Prague, Czech Republic (2018).
[ pdf ]

Colorful Graph Theory [invited talk],
19. Konferencia košických matematikov, Herl'any, Slovakia (2018).
[ pdf ]

Edgecolorings as edgedecompositions,
Ljubljana  Leoben Graph Theory Seminar 2017, Maribor, Slovenia (2017).

Edgecolorings as edgedecompositions,
Cycles and Colourings, High Tatras, Slovakia (2017).
[ pdf ]

Results on locally irregular edgecoloring,
The 52nd CzechSlovak Conference on Combinatorics and Graph Theory, Hejnice, Czech Republic (2017).
[ pdf ]

Edgecoloring Variations [invited talk],
II Studencka Konferencja KNDM, Krakow, Poland (2017).
[ pdf ]

Edgecolorings: Results & Problems,
Workshop on Graph Colourings, Plzeň, Czech Republic (2017).
[ Prezi ]

Locally irregular edgecoloring & 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,
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 CzechSlovak International Symposium on Graph Theory, Combinatorics, Algorithms and Applications, Košice, Slovakia (2013).
[ pdf ]
Seminar talks
Some of my most recent seminar talks outside my affiliating institutions are listed.

Some coloring properties of medial graphs,
Košický kombinatorický seminár, Košice, Slovakia (2018).
[ pdf ]

3choosability 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).
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,
Marek Cygan,
Darko Dimitrov,
Tomislav Došlić,
François Dross,
Jiři Fink,
Tanja Gologranc,
Petr Gregor,
Ivan Gutman,
David Hudák,
Maria Janicová,
František Kardoš,
Mario Karlovčec,
Andrej Kastrin,
Jelena Klisara,
Martin Knor,
Łukasz Kowalik,
Daniel Kraĺ,
Matjaž Krnc,
Jaka Kranjc,
Martin Kupec,
Zoran Levnajić,
Bernard Lidický,
Tomaš Madaras,
Luka Mali,
Dunja Mladenić,
Martina Mockovčiaková,
Pascal Ochem,
Alenka Pandiloska Jurak,
Matjaž Perc,
Mirko Petruševski,
Alexandre Pinlou,
Janez Povh,
Jakub Przybyło,
Edo Ravnikar,
Martin Ravnikar,
Roman Soták,
Ľudmila Šebestová,
Riste Škrekovski,
Roman Šoper,
Peter Šugerek,
Martin Tancer,
Jan Volec.
Useful links