Longest circuits in triangular and quadrangular 3 -polytopes with two types of edges

Stanislav Jendroľ; Roman Kekeňák

Mathematica Slovaca (1990)

  • Volume: 40, Issue: 4, page 341-357
  • ISSN: 0139-9918

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Jendroľ, Stanislav, and Kekeňák, Roman. "Longest circuits in triangular and quadrangular $3$-polytopes with two types of edges." Mathematica Slovaca 40.4 (1990): 341-357. <http://eudml.org/doc/31774>.

@article{Jendroľ1990,
author = {Jendroľ, Stanislav, Kekeňák, Roman},
journal = {Mathematica Slovaca},
keywords = {connectivity; longest circuits; 3-polytopes; Hamiltonicity},
language = {eng},
number = {4},
pages = {341-357},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Longest circuits in triangular and quadrangular $3$-polytopes with two types of edges},
url = {http://eudml.org/doc/31774},
volume = {40},
year = {1990},
}

TY - JOUR
AU - Jendroľ, Stanislav
AU - Kekeňák, Roman
TI - Longest circuits in triangular and quadrangular $3$-polytopes with two types of edges
JO - Mathematica Slovaca
PY - 1990
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 40
IS - 4
SP - 341
EP - 357
LA - eng
KW - connectivity; longest circuits; 3-polytopes; Hamiltonicity
UR - http://eudml.org/doc/31774
ER -

References

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  1. EWALD G., Hamiltonian circuits in simplicial complexes, Geometriae Dedicata 2, 1973, 115-125. (1973) Zbl0272.57008MR0320891
  2. EWALD G., On shortness exponents of families of graphs, Israel J. Math., 16, 1973, 53-61. (1973) Zbl0271.05107MR0344152
  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. (1979) MR0568497
  4. GRÜNBAUM B., Convex polytopes, Wiley, New York 1967. (1967) Zbl0163.16603MR0226496
  5. GRÜNBAUM B., Polytopes, graphs, and complexes, Bull. Amer. Math. Soc. 76, 1970, 1131-1201. (1970) Zbl0211.25001MR0266050
  6. GRÜNBAUM B., MALKEVITCH J., Pairs of edge-disjoint Hamiltonian circuits, Aequatines Math. 14, 1976, 191 - 196. (1976) Zbl0331.05118MR0414443
  7. GRÜNBAUM B., WALTHER H., Shortness exponents of families of graphs, J. Combinatorial Theory (A) 14, 1973, 364-385. (1973) Zbl0263.05103MR0314691
  8. HARANT J., WALTHER H., Some new results about the shortness exponent in polyhedra graphs, Čas. pěst. mat., 112, 1987, 114-122. (1987) MR0897639
  9. JACKSON B., Longest cycles in 3-connected cubic graphs, J. Combinatorial Theory (B) 41 1986, 17-26. (1986) Zbl0591.05040MR0854600
  10. JENDROĽ S., JUCOVIČ E., On quadrangular convex 3-polytopes with at most two types of edges, Discrete Math. 78, 1989, 297-305. (1989) Zbl0691.52004MR1026349
  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. (1989) Zbl0705.05043MR1097639
  12. JENDROĽ S., MIHÓK P., On a class of Hamiltonian polytopes, Discrete Math. 71, 1988, 233-241. (1988) Zbl0655.05045MR0959008
  13. JENDROĽ S., TKÁČ M., On the simplicial 3-polytopes with only two types of edges, Discrete Math. 48, 1984, 229-241. (1984) Zbl0536.52003MR0737268
  14. JUCOVIČ E., Konvexné mnohosteny, Veda, Bratislava, 1981 (in Slovak). (1981) 
  15. ORE O., The four-color problem, Academic Press, New York-London, 1967. (1967) Zbl0149.21101MR0216979
  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. (1982) MR0675864
  17. OWENS P. J., Regular planar graphs with faces of only two types and shortness parameters, J. Graph Theory 8, 1984, 253-275. (1984) Zbl0541.05037MR0742879
  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. (1984) Zbl0571.05033MR0791037
  19. OWENS P. J., Simple 3-polytopal graphs with edges of only two types and shortness coefficients, Discrete Math. 59, 1986, 107-114. (1986) Zbl0586.05027MR0837960
  20. PAREEK C. M., On the maximum degree of locally hamiltonian non-hamiltonian graphs, Utilitas Mathematica 23, 1983, 101-120. (1983) Zbl0523.05048MR0703133
  21. TRENKLER M., On the face-vector of a 5-valent convex 3-polytope, Mat. Časopis 25, 1975, 351-360. (1975) Zbl0313.52004MR0467535
  22. ZAKS J., Shortness coeffìcient of cyclically 5-connected cubic planar graphs, Aequationes Math. 25, 1982, 97-102. (1982) Zbl0518.05045MR0716382

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