| Title:
|
Longest circuits in triangular and quadrangular $3$-polytopes with two types of edges (English) |
| Author:
|
Jendroľ, Stanislav |
| Author:
|
Kekeňák, Roman |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
40 |
| Issue:
|
4 |
| Year:
|
1990 |
| Pages:
|
341-357 |
| . |
| Category:
|
math |
| . |
| MSC:
|
05C40 |
| MSC:
|
05C45 |
| idZBL:
|
Zbl 0757.05073 |
| idMR:
|
MR1120965 |
| . |
| Date available:
|
2009-09-25T10:26:29Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/129289 |
| . |
| Reference:
|
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| Reference:
|
[2] EWALD G.: On shortness exponents of families of graphs.Israel J. Math., 16, 1973, 53-61. Zbl 0271.05107, MR 0344152 |
| Reference:
|
[3] EWALD G., KLEINSCHMIDT P., PACHNER U., SCHULZ, CH.: Neuere Entwick- lungen in der kombinatorischen Konvexgeometrie.Contributions to geometry (ed. J. Tolke, J. M. Wills), Birkhäuser Verlag, Basel 1979, 131-169. MR 0568497 |
| Reference:
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[4] GRÜNBAUM B.: Convex polytopes.Wiley, New York 1967. Zbl 0163.16603, MR 0226496 |
| Reference:
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[5] GRÜNBAUM B.: Polytopes, graphs, and complexes.Bull. Amer. Math. Soc. 76, 1970, 1131-1201. Zbl 0211.25001, MR 0266050 |
| Reference:
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[6] GRÜNBAUM B., MALKEVITCH J.: Pairs of edge-disjoint Hamiltonian circuits.Aequatines Math. 14, 1976, 191 - 196. Zbl 0331.05118, MR 0414443 |
| Reference:
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[7] GRÜNBAUM B., WALTHER H.: Shortness exponents of families of graphs.J. Combinatorial Theory (A) 14, 1973, 364-385. Zbl 0263.05103, MR 0314691 |
| Reference:
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[8] HARANT J., WALTHER H.: Some new results about the shortness exponent in polyhedra graphs.Čas. pěst. mat., 112, 1987, 114-122. MR 0897639 |
| Reference:
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[9] JACKSON B.: Longest cycles in 3-connected cubic graphs.J. Combinatorial Theory (B) 41 1986, 17-26. Zbl 0591.05040, MR 0854600 |
| Reference:
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[10] JENDROĽ S., JUCOVIČ E.: On quadrangular convex 3-polytopes with at most two types of edges.Discrete Math. 78, 1989, 297-305. Zbl 0691.52004, MR 1026349 |
| Reference:
|
[11] JENDROĽ S., JUCOVIČ E., TRENKLER M.: Vertex-vectors of quadrangular 3-polytopes with two types of edges.Combinatories and Graph Theory, Banach Center Publications, Vol. 25, PWN - Polish Scientific Publishers, Warsaw 1989, 93-111. Zbl 0705.05043, MR 1097639 |
| Reference:
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[12] JENDROĽ S., MIHÓK P.: On a class of Hamiltonian polytopes.Discrete Math. 71, 1988, 233-241. Zbl 0655.05045, MR 0959008 |
| Reference:
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[13] JENDROĽ S., TKÁČ M.: On the simplicial 3-polytopes with only two types of edges.Discrete Math. 48, 1984, 229-241. Zbl 0536.52003, MR 0737268 |
| Reference:
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[14] JUCOVIČ E.: Konvexné mnohosteny.Veda, Bratislava, 1981 (in Slovak). |
| Reference:
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[15] ORE O.: The four-color problem.Academic Press, New York-London, 1967. Zbl 0149.21101, MR 0216979 |
| Reference:
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[16] OWENS P. J.: Shortness parameters of families of regular planar graphs with two or three types of faces.Discrete Math. 39, 1982, 199-201. MR 0675864 |
| Reference:
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[17] OWENS P. J.: Regular planar graphs with faces of only two types and shortness parameters.J. Graph Theory 8, 1984, 253-275. Zbl 0541.05037, MR 0742879 |
| Reference:
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[18] OWENS P. J.: Non-hamiltonian simple 3-polytopes with only one type of face besides triangles.Annals of Discrete Math. 20, 1984, 241-251. Zbl 0571.05033, MR 0791037 |
| Reference:
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[19] OWENS P. J.: Simple 3-polytopal graphs with edges of only two types and shortness coefficients.Discrete Math. 59, 1986, 107-114. Zbl 0586.05027, MR 0837960 |
| Reference:
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[20] PAREEK C. M.: On the maximum degree of locally hamiltonian non-hamiltonian graphs.Utilitas Mathematica 23, 1983, 101-120. Zbl 0523.05048, MR 0703133 |
| Reference:
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[21] TRENKLER M.: On the face-vector of a 5-valent convex 3-polytope.Mat. Časopis 25, 1975, 351-360. Zbl 0313.52004, MR 0467535 |
| Reference:
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[22] ZAKS J.: Shortness coeffìcient of cyclically 5-connected cubic planar graphs.Aequationes Math. 25, 1982, 97-102. Zbl 0518.05045, MR 0716382 |
| . |
