Roman Nedela

    Institute of Mathematics and Computer Science
Ďumbierska 1
974 11 Banská Bystrica
Slovak republic

e-mail: nedela at savbb.sk (at = @)
Phone : (+421 48) 415 10 12

Curriculum Vitae List of Publications Teaching Projects

 

Links

Lectures

Graphs and Their Symmetries

1. Graphs and Their Coverings

Grafy s polhranami, fundamentalna grupa grafu s polhranami, nakrytia grafov a ich kombinatoricky opis, grupa automorfizmov grafu, vztah regularnych kvocientov a obycajnych napatovych grafov, Cayleyho a Schreierove grafy. Problem zdvihania a projekcie automorfizmu grafu. Pouzitie nakryti grafov na riesenie niektorych problemov z teorie grafov.

2. Graph Embeddings and Maps on Surfaces

Klasifikacia ploch, celularne vnorenie grafu, Euler-Poincareho veta, kombinatoricky opis map, dve kategorie map, rozvetvene nakrytia ploch a morfizmy map, interpolacna veta, minimalny a maximalny rod, triangulacie, Heawoodov problem, hypermapy a ich modely.

3. Symmetries of Maps

Mapy a grupy, grupa monodromie mapy, regularne a vrcholovo tranzitivne mapy, mapy a trojuholnikove grupy, univerzalne nakrytia, mapy typu (p,q), rezidualna konecnost trojuholnikovych grup, permutacny a maticovy pristup, Riemann-Hurwitzova veta a jej dosledky.

4. Classification and Enumeration Problems
5. Manifolds of Higher Dimension

Problem homeomorfizmu topologickych n-variet a jeho kombinatoricky ekvivalent, Heegaardov rod, 3-variety rodu najviac dva.


References:
1. J.L. Gross, T.W. Tucker, Topological graph theory, Dover Publications New York, 2001. ( k temam 1 a 2)

2. Malnic,A.-Nedela,R.-Skoviera,M.: Lifting graph automorphisms by voltage assignments, European J. Combin. 21, 2000, 927-947. ( k teme 1)

3. G. Jones, D. Singerman, Theory of maps on orientable surfaces, Proc. London Math. Soc. 37, 1978, 273-307. ( k teme 3)

4. Nedela,R.-Skoviera,M.: Exponents of orientable maps, Proceedings of London Math. Soc. (3) 75, 1997, 1-31. (k teme 3 a 5)

5. J. Siran, Regular maps, Lecture Notes Ser., Combinatorial and Computational Math. Center, Pohang 2001. (k temam 3 a 4)

6. Malnic,A.-Nedela,R.-Skoviera,M.: Regular homomorphisms and regular maps, European J. Combin. 23 (4), 2002, 449-461. ( k teme 3)

7. Gardiner,A.-Nedela,R.-Sirán,J.-Skoviera,M: Characterization of graphs which underlie regular maps on closed surfaces. J. London Math. Soc. 59 (1), 1999, 100-108. ( k teme 7)

8. Breda,A.-Nedela,R.: Join and intersection of hypermaps, Acta Univ. Math. Belii, Ser Math. 9, 2001, 13-28. (k teme 6)

9. Bandieri, P., Casali, M. R. and Gagliardi, C., Representing Manifolds by Crystallisation Theory: Foundations, Improvements and Related Results, Atti Sem. Mat. Fis. Univ. Modena IL (2001), 283-337. (k teme 8)

Cielom predmetu je vybudovat zaklady topologickej teorie grafov, pricom doraz bude kladeny na otazky a suvislosti tejto teorie s teoriou grup. Urcity priestor bude venovany ukazkam pouzitia teorie na riesenie konkretnych problemov v teorii grafov, teorii grup. Suvisu s komplexnou analyzou a topologiou sa budeme venovat len okrajovo. Znacny priestor budeme venovat klasifikacnym problemom tykahucich sa vysokosymetrickych map. Kazdu temu ukoncime diskusiou o otvorenych problemoch a sucasnom stave problematiky.
Podrobnejsie sylaby prednasok budu spristupnene priebezne na web stranke.
 

 

Projects

1. VEGA 2/2060/22,
Algebraic and Combinatoric Properties of Graphs, Maps, Posets and Related Structures. Principal Investigator : Nedela

2. APVT-51-012502,
Discrete Structures Representation and their Applications. Principal Investigator : Nedela
Final grant report(in slovak)