| Title:
|
On face-vectors and vertex-vectors of polyhedral maps on orientable $2$-manifolds (English) |
| Author:
|
Jendroľ, Stanislav |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
1993 |
| Pages:
|
393-416 |
| . |
| Category:
|
math |
| . |
| MSC:
|
05C10 |
| MSC:
|
52B70 |
| idZBL:
|
Zbl 0795.05049 |
| idMR:
|
MR1248974 |
| . |
| Date available:
|
2009-09-25T10:50:03Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/132351 |
| . |
| Reference:
|
[1] BARNETTE D.: On p-vectors of 3-polytopes.J. Combin. Theory Ser.? 7 (1969), 89-103. Zbl 0179.25902, MR 0244851 |
| Reference:
|
[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. Zbl 0491.05027, MR 0650299 |
| Reference:
|
[3] EBERHARD V.: Zur Morphologie der Polyeder.Teubner, Leipzig, 1891. |
| Reference:
|
[4] ENNS T. C.: Convex 4-valent polytopes.Discrete Math. 30 (1980), 227-234. Zbl 0441.52006, MR 0573637 |
| Reference:
|
[5] ENNS T. C.: 4-valent graphs.J. Graph Theory 6 (1982), 255-281. Zbl 0457.05058, MR 0666795 |
| Reference:
|
[6] FISHER J. C.: An existence theorem for simple convex polyhedra.Discrete Math. 7 (1974), 75-97. Zbl 0271.52008, MR 0333984 |
| Reference:
|
[7] GRITZMANN P.: The toroidal analogue to Eberhard's theorem.Mathematika 30 (1983), 274-290. Zbl 0519.57015, MR 0737179 |
| Reference:
|
[8] GRÜNBAUM B.: Convex Polytopes.Interscience, New York, 1967. MR 0226496 |
| Reference:
|
[9] GRÜNBAUM B.: Some analogues of Eberhard's theorem on convex polytopes.Israel J. Math. 6 (1968), 398-411. MR 0244854 |
| Reference:
|
[10] GRÜNBAUM B.: Planar maps with prescribed types of vertices and faces.Mathematika 16 (1969), 28-36. Zbl 0186.27502, MR 0245460 |
| Reference:
|
[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. Zbl 0323.05104, MR 0406868 |
| Reference:
|
[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. MR 0154182 |
| Reference:
|
[13] GRÜNBAUM B., SHEPHARD G. C.: The theorems of Euler and Eberhard for tilings of the plane.Resultate Math. 5 (1982), 19-44. Zbl 0505.52004, MR 0662793 |
| Reference:
|
[14] GRÜNBAUM B., ZAKS J.: The existence of certain planar maps.Discrete Math. 10 (1974), 93-115. Zbl 0298.05112, MR 0349455 |
| Reference:
|
[15] JENDROE S.: On the face-vector of trivalent convex polyhedra.Math. Slovaca 33 (1983), 165-180. MR 0699086 |
| Reference:
|
[16] JENDROE S.: On face vectors of trivalent maps.Math. Slovaca 36 (1986), 367-386. MR 0871777 |
| Reference:
|
17] JENDROE S.: On face-vectors and vertex-vectors of convex polyhedra.Discrete Math. 118 (1993), 119-144. MR 1230057 |
| Reference:
|
[18] JENDROE S., JUCOVIČ E.: On a conjecture by B. Grünbaum.Discrete Math. 2 (1972), 35-49. MR 0302497 |
| Reference:
|
[19] JENDROE S., JUCOVIČ E.: Generalization of a theorem by V. Eberhard.Math. Slovaca 27 (1977), 383-407. MR 0536841 |
| Reference:
|
[20] JUCOVIČ E.: On the number of hexagons in a map.J. Combin. Theory Ser. B 10 (1971), 232-236. Zbl 0214.50902, MR 0278179 |
| Reference:
|
[21] JUCOVIČ E.: On face-vectors and vertex-vectors of cell-decompositions of orientable 2-manifolds.Math. Nachr. 73 (1976), 285-295. Zbl 0337.55003, MR 0432490 |
| Reference:
|
[22] JUCOVIČ E.: Convex 3-polytopes.(Slovak), Veda, Bratislava, 1981. |
| Reference:
|
[23] KRAEFT J.: Über 3-realisierbare Folgen mit beliebigen Sechseckzahlen.J. Geom. 10 (1977), 32-44. Zbl 0357.52008, MR 0513982 |
| Reference:
|
[24] MALKEVITCH J.: Polytopal graphs.In: Selected Topics in Graph Theory 3, Academic Press, London, 1988, pp. 169-188. Zbl 0678.05015, MR 1205401 |
| Reference:
|
[25] TRENKLER M.: Convex 4-valent polytopes with prescribed types of faces.Comment. Math. Univ. Carolin. 25 (1984), 171-179. Zbl 0551.52005, MR 0749125 |
| . |
