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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 |
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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 |
LinksLecturesGraphs and Their Symmetries1. 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 SurfacesKlasifikacia 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 MapsMapy 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 Problems5. 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. |
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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) |