On face-vectors and vertex-vectors of polyhedral maps on orientable 2 -manifolds

Stanislav Jendroľ

Mathematica Slovaca (1993)

  • Volume: 43, Issue: 4, page 393-416
  • ISSN: 0232-0525

How to cite

top

Jendroľ, Stanislav. "On face-vectors and vertex-vectors of polyhedral maps on orientable $2$-manifolds." Mathematica Slovaca 43.4 (1993): 393-416. <http://eudml.org/doc/32279>.

@article{Jendroľ1993,
author = {Jendroľ, Stanislav},
journal = {Mathematica Slovaca},
keywords = {polyhedral map; orientable 2-manifold; genus; vertex-vector; face-vector},
language = {eng},
number = {4},
pages = {393-416},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {On face-vectors and vertex-vectors of polyhedral maps on orientable $2$-manifolds},
url = {http://eudml.org/doc/32279},
volume = {43},
year = {1993},
}

TY - JOUR
AU - Jendroľ, Stanislav
TI - On face-vectors and vertex-vectors of polyhedral maps on orientable $2$-manifolds
JO - Mathematica Slovaca
PY - 1993
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 43
IS - 4
SP - 393
EP - 416
LA - eng
KW - polyhedral map; orientable 2-manifold; genus; vertex-vector; face-vector
UR - http://eudml.org/doc/32279
ER -

References

top
  1. BARNETTE D., On p-vectors of 3-polytopes, J. Combin. Theory Ser.? 7 (1969), 89-103. (1969) Zbl0179.25902MR0244851
  2. BARNETTE D., Polyhedral maps on 2-manifolds, In: Convexity and Related Combinatorial Geometry (D. C. Kay and M. Breen, eds.), Marcel Dekker Inc., New York and Basel, 1982, pp. 7-19. (1982) Zbl0491.05027MR0650299
  3. EBERHARD V., Zur Morphologie der Polyeder, Teubner, Leipzig, 1891. 
  4. ENNS T. C., Convex 4-valent polytopes, Discrete Math. 30 (1980), 227-234. (1980) Zbl0441.52006MR0573637
  5. ENNS T. C., 4-valent graphs, J. Graph Theory 6 (1982), 255-281. (1982) Zbl0457.05058MR0666795
  6. FISHER J. C., An existence theorem for simple convex polyhedra, Discrete Math. 7 (1974), 75-97. (1974) Zbl0271.52008MR0333984
  7. GRITZMANN P., The toroidal analogue to Eberhard's theorem, Mathematika 30 (1983), 274-290. (1983) Zbl0519.57015MR0737179
  8. GRÜNBAUM B., Convex Polytopes, Interscience, New York, 1967. (1967) MR0226496
  9. GRÜNBAUM B., Some analogues of Eberhard's theorem on convex polytopes, Israel J. Math. 6 (1968), 398-411. (1968) MR0244854
  10. GRÜNBAUM B., Planar maps with prescribed types of vertices and faces, Mathematika 16 (1969), 28-36. (1969) Zbl0186.27502MR0245460
  11. GRÜNBAUM B., Polytopal graphs, In: Studies in Graph Theory MAA Stud. Math. 12 (D. R. Fulkerson, ed.), Math. Assoc. America, Washington, DC, 1975, pp. 201-224. (1975) Zbl0323.05104MR0406868
  12. GRÜNBAUM B., MOTZKIN T. S., The number of hexagons and the simplicity of geodesies of certain polyhedra, Canad. J. Math. 15 (1963), 744-751. (1963) MR0154182
  13. GRÜNBAUM B., SHEPHARD G. C., The theorems of Euler and Eberhard for tilings of the plane, Resultate Math. 5 (1982), 19-44. (1982) Zbl0505.52004MR0662793
  14. GRÜNBAUM B., ZAKS J., The existence of certain planar maps, Discrete Math. 10 (1974), 93-115. (1974) Zbl0298.05112MR0349455
  15. JENDROE S., On the face-vector of trivalent convex polyhedra, Math. Slovaca 33 (1983), 165-180. (1983) MR0699086
  16. JENDROE S., On face vectors of trivalent maps, Math. Slovaca 36 (1986), 367-386. (1986) MR0871777
  17. 17] JENDROE S., On face-vectors and vertex-vectors of convex polyhedra, Discrete Math. 118 (1993), 119-144. (1993) MR1230057
  18. JENDROE S., JUCOVIČ E., On a conjecture by B. Grünbaum, Discrete Math. 2 (1972), 35-49. (1972) MR0302497
  19. JENDROE S., JUCOVIČ E., Generalization of a theorem by V. Eberhard, Math. Slovaca 27 (1977), 383-407. (1977) MR0536841
  20. JUCOVIČ E., On the number of hexagons in a map, J. Combin. Theory Ser. B 10 (1971), 232-236. (1971) Zbl0214.50902MR0278179
  21. JUCOVIČ E., On face-vectors and vertex-vectors of cell-decompositions of orientable 2-manifolds, Math. Nachr. 73 (1976), 285-295. (1976) Zbl0337.55003MR0432490
  22. JUCOVIČ E., Convex 3-polytopes, (Slovak), Veda, Bratislava, 1981. (1981) 
  23. KRAEFT J., Über 3-realisierbare Folgen mit beliebigen Sechseckzahlen, J. Geom. 10 (1977), 32-44. (1977) Zbl0357.52008MR0513982
  24. MALKEVITCH J., Polytopal graphs, In: Selected Topics in Graph Theory 3, Academic Press, London, 1988, pp. 169-188. (1988) Zbl0678.05015MR1205401
  25. TRENKLER M., Convex 4-valent polytopes with prescribed types of faces, Comment. Math. Univ. Carolin. 25 (1984), 171-179. (1984) Zbl0551.52005MR0749125

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.