Constructing regular maps and graphs from planar quotients

Stanislav Jendroľ; Roman Nedela; Martin Škoviera

Mathematica Slovaca (1997)

  • Volume: 47, Issue: 2, page 155-170
  • ISSN: 0232-0525

How to cite

top

Jendroľ, Stanislav, Nedela, Roman, and Škoviera, Martin. "Constructing regular maps and graphs from planar quotients." Mathematica Slovaca 47.2 (1997): 155-170. <http://eudml.org/doc/34455>.

@article{Jendroľ1997,
author = {Jendroľ, Stanislav, Nedela, Roman, Škoviera, Martin},
journal = {Mathematica Slovaca},
keywords = {regular map; covering projection; face-width; graph automorphism; girth of a graph; cubic graph},
language = {eng},
number = {2},
pages = {155-170},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Constructing regular maps and graphs from planar quotients},
url = {http://eudml.org/doc/34455},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Jendroľ, Stanislav
AU - Nedela, Roman
AU - Škoviera, Martin
TI - Constructing regular maps and graphs from planar quotients
JO - Mathematica Slovaca
PY - 1997
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 47
IS - 2
SP - 155
EP - 170
LA - eng
KW - regular map; covering projection; face-width; graph automorphism; girth of a graph; cubic graph
UR - http://eudml.org/doc/34455
ER -

References

top
  1. ARCHDEACON D., Densely embedded graphs, J. Combin. Theory Ser. B 54 (1992), 13-36. (1992) Zbl0694.05024MR1142262
  2. ARCHDEACON D.-GVOZDJAK P.-ŠIRÁŇ J., Constructing and forbidding automorphisms in lifted maps, Math. Slovaca 47 (1997), 113-129. (1997) Zbl1053.05503MR1476862
  3. BIGGS N. L., Girth and residual fìniteness, Combinatorica 8 (1988), 307-312. (1988) Zbl0712.05035MR0981888
  4. BIGGS N. L., Cubic graphs with large girth, In: Ann. New York Acad. Sci. 555, New York Acad. Sci.-New York, 1989, pp. 56-62. (1989) Zbl0731.05026MR1018609
  5. BROWN M.-CONNELLY R., On graphs with a constant link, In: New Directions in the Theorу of Graphs (F. Harary, ed.), Academic Press, New York, 1973, pp. 19-51. (1973) Zbl0258.05104MR0347685
  6. CONDER M., Hurwitz groups: a brief survey, Bull. Amer. Math. Soc. 23 (1990), 359-370. (1990) Zbl0716.20015MR1041434
  7. COXETER H. S. M.-MOSER W. O., Generators and Relations for Discrete Groups, (Зrd ed.), Springer, Berlin, 1972. (1972) Zbl0239.20040MR0349820
  8. FOX R. H., On Fencheľs conjecture about F-groups, Mat. Tidskrift B (1952), 61-65. (1952) MR0053937
  9. GARDINER A.-NEDELA R.-ŠIRÁŇ J.-ŠKOVIERA M., Characterization of graphs which underlie regular maps on closed surfaces, J. London Math. Soc. (To appear). MR1688492
  10. GRAY A.-WILSON S., A more elementary proof of Grünbaum's conjecture, Congr. Numer. 72 (1990), 25-32. (1990) Zbl0716.05015MR1041804
  11. GROSS J. L.-TUCKER T. W., Topological Graph Theory, Wiley, New York, 1987. (1987) Zbl0621.05013MR0898434
  12. GROTHEDIECK A., Esquisse d'un programme, Preprint, Montpellier, 1984. (1984) 
  13. GRÜNBAUM B., Regularity of graphs, complexes and designs, In: Problèmes combinatoires et théorie des graphes, Colloques Internationaux C.N.R.S. 260, Paris, 1978, pp. 191-197. (1978) Zbl0419.05017MR0539975
  14. JONES G. A.-SINGERMAN D., Theory of maps on orientable surfaces, Proc. London Math. Soc. (3) 37 (1978), 273-307. (1978) Zbl0391.05024MR0505721
  15. KAPLANSKY I., Commutative Rings, University of Chicago Press, Chicago, 1974. (1974) Zbl0296.13001MR0345945
  16. MacBEATH A. M., Generators of linear fractional groups, In: Proc. Sympos. Pure Math., Vol. XII, Amer. Math. Soc, Providence, R.I., 1969, pp. 14-32. (1969) MR0262379
  17. MOHAR B., Face-width of embedded graphs, Math. Slovaca 47 (1997), 35-63. (1997) Zbl0958.05034MR1476747
  18. NEDELA R., Graphs which are edge-locally Cn, Math. Slovaca (To appear). MR1796951
  19. NEDELA R.-SKOVIERA M., Atoms of cyclic connectivity in transitive cubic graphs, In: Contemporary Methods in Graph Theory (R. Bodendiek, ed.) (in honour of K. Wagner), BI-Wissenschaftsverlag, Mannheim, 1990, pp. 479-488. (1990) Zbl0717.05049MR1126248
  20. NEDELA R.-SKOVIERA M., Atoms of cyclic connectivity in cubic graphs, Math. Slovaca 45 (1995), 481-489. (1995) Zbl0844.05066MR1390702
  21. NEDELA R.-SKOVIERA M., Exponents of orientable maps, Proc. London Math. Soc. (3) 75 (1997), 1-31. (1997) Zbl0877.05012MR1444311
  22. NEGAMI S., Uniqueness and Faithfulness of Embedding of Graphs into Surfaces, PhD. Thesis, Tokyo Institute of Technology, Tokyo, 1985. (1985) 
  23. PARSONS T. D.-PISANSKI T., Graphs which are locally paths, In: Combinatorics and Graph Theory (Z. Skupieri, M. Borowiecki, eds.), Banach Center Publ. 25, PWN - Pol. Sci. Publ., Warsaw, 1989, pp. 163-175. (1989) Zbl0757.05071MR1097642
  24. PERKEL M., Trivalent polygonal graphs, Congr. Numer. 45 (1984), 45-70. (1984) Zbl0571.05016MR0777711
  25. PERKEL M., Trivalent polygonal grapgs of girth 6 and 7, Congr. Numer. 49 (1985), 129-138. (1985) MR0830736
  26. SUROWSKI D., Lifting map automorphisms and MacBeath's theorem, J. Combin. Theory Ser. B 50 (1990), 135-149. (1990) Zbl0735.05034MR1081218
  27. VINCE A., Regular combinatorial maps, J. Combin. Theory Ser. B 35 (1983), 256-277. (1983) Zbl0514.05032MR0735194
  28. WILSON S., A construction from an existence proof, Congr. Numer. 50 (1985), 25-30. (1985) Zbl0594.52011MR0833533
  29. WILSON S., Applications and refinements of Vince's construction, Geom. Dedicata 48 (1993), 231-242. (1993) Zbl0792.51012MR1248905

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.