On face-vectors and vertex-vectors of polyhedral maps on orientable -manifolds
Mathematica Slovaca (1993)
- Volume: 43, Issue: 4, page 393-416
- ISSN: 0232-0525
Access Full Article
topHow to cite
topJendroľ, 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- BARNETTE D., On p-vectors of 3-polytopes, J. Combin. Theory Ser.? 7 (1969), 89-103. (1969) Zbl0179.25902MR0244851
- 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
- EBERHARD V., Zur Morphologie der Polyeder, Teubner, Leipzig, 1891.
- ENNS T. C., Convex 4-valent polytopes, Discrete Math. 30 (1980), 227-234. (1980) Zbl0441.52006MR0573637
- ENNS T. C., 4-valent graphs, J. Graph Theory 6 (1982), 255-281. (1982) Zbl0457.05058MR0666795
- FISHER J. C., An existence theorem for simple convex polyhedra, Discrete Math. 7 (1974), 75-97. (1974) Zbl0271.52008MR0333984
- GRITZMANN P., The toroidal analogue to Eberhard's theorem, Mathematika 30 (1983), 274-290. (1983) Zbl0519.57015MR0737179
- GRÜNBAUM B., Convex Polytopes, Interscience, New York, 1967. (1967) MR0226496
- GRÜNBAUM B., Some analogues of Eberhard's theorem on convex polytopes, Israel J. Math. 6 (1968), 398-411. (1968) MR0244854
- GRÜNBAUM B., Planar maps with prescribed types of vertices and faces, Mathematika 16 (1969), 28-36. (1969) Zbl0186.27502MR0245460
- 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
- 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
- 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
- GRÜNBAUM B., ZAKS J., The existence of certain planar maps, Discrete Math. 10 (1974), 93-115. (1974) Zbl0298.05112MR0349455
- JENDROE S., On the face-vector of trivalent convex polyhedra, Math. Slovaca 33 (1983), 165-180. (1983) MR0699086
- JENDROE S., On face vectors of trivalent maps, Math. Slovaca 36 (1986), 367-386. (1986) MR0871777
- 17] JENDROE S., On face-vectors and vertex-vectors of convex polyhedra, Discrete Math. 118 (1993), 119-144. (1993) MR1230057
- JENDROE S., JUCOVIČ E., On a conjecture by B. Grünbaum, Discrete Math. 2 (1972), 35-49. (1972) MR0302497
- JENDROE S., JUCOVIČ E., Generalization of a theorem by V. Eberhard, Math. Slovaca 27 (1977), 383-407. (1977) MR0536841
- JUCOVIČ E., On the number of hexagons in a map, J. Combin. Theory Ser. B 10 (1971), 232-236. (1971) Zbl0214.50902MR0278179
- JUCOVIČ E., On face-vectors and vertex-vectors of cell-decompositions of orientable 2-manifolds, Math. Nachr. 73 (1976), 285-295. (1976) Zbl0337.55003MR0432490
- JUCOVIČ E., Convex 3-polytopes, (Slovak), Veda, Bratislava, 1981. (1981)
- KRAEFT J., Über 3-realisierbare Folgen mit beliebigen Sechseckzahlen, J. Geom. 10 (1977), 32-44. (1977) Zbl0357.52008MR0513982
- MALKEVITCH J., Polytopal graphs, In: Selected Topics in Graph Theory 3, Academic Press, London, 1988, pp. 169-188. (1988) Zbl0678.05015MR1205401
- TRENKLER M., Convex 4-valent polytopes with prescribed types of faces, Comment. Math. Univ. Carolin. 25 (1984), 171-179. (1984) Zbl0551.52005MR0749125
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.