Some news about oblique graphs

Andrey A. Dobrynin; Leonid S. Melnikov; Jens Schreyer; Hansjoachim Walther

Discussiones Mathematicae Graph Theory (2002)

  • Volume: 22, Issue: 1, page 39-50
  • ISSN: 2083-5892

Abstract

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A k-gon α of a polyhedral graph G(V,E,F) is of type ⟨b₁,b₂,...,bₖ⟩ if the vertices incident with α in cyclic order have degrees b₁,b₂,...,bₖ and ⟨b₁,b₂,...,bₖ⟩ is the lexicographic minimum of all such sequences available for α. A polyhedral graph G is oblique if it has no two faces of the same type. Among others it is shown that an oblique graph contains vertices of degree 3.

How to cite

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Andrey A. Dobrynin, et al. "Some news about oblique graphs." Discussiones Mathematicae Graph Theory 22.1 (2002): 39-50. <http://eudml.org/doc/270516>.

@article{AndreyA2002,
abstract = {A k-gon α of a polyhedral graph G(V,E,F) is of type ⟨b₁,b₂,...,bₖ⟩ if the vertices incident with α in cyclic order have degrees b₁,b₂,...,bₖ and ⟨b₁,b₂,...,bₖ⟩ is the lexicographic minimum of all such sequences available for α. A polyhedral graph G is oblique if it has no two faces of the same type. Among others it is shown that an oblique graph contains vertices of degree 3.},
author = {Andrey A. Dobrynin, Leonid S. Melnikov, Jens Schreyer, Hansjoachim Walther},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {polyhedral graph; oblique graph; triangulation},
language = {eng},
number = {1},
pages = {39-50},
title = {Some news about oblique graphs},
url = {http://eudml.org/doc/270516},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Andrey A. Dobrynin
AU - Leonid S. Melnikov
AU - Jens Schreyer
AU - Hansjoachim Walther
TI - Some news about oblique graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2002
VL - 22
IS - 1
SP - 39
EP - 50
AB - A k-gon α of a polyhedral graph G(V,E,F) is of type ⟨b₁,b₂,...,bₖ⟩ if the vertices incident with α in cyclic order have degrees b₁,b₂,...,bₖ and ⟨b₁,b₂,...,bₖ⟩ is the lexicographic minimum of all such sequences available for α. A polyhedral graph G is oblique if it has no two faces of the same type. Among others it is shown that an oblique graph contains vertices of degree 3.
LA - eng
KW - polyhedral graph; oblique graph; triangulation
UR - http://eudml.org/doc/270516
ER -

References

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  1. [1] O. Borodin, Structural properties of planar maps with the minimum degree 5, Math. Nachr. 158 (1992) 109-117, doi: 10.1002/mana.19921580108. Zbl0776.05035
  2. [2] B. Grünbaum and C.J. Shephard, Spherical tilings with transitivity properties, in: Geometrie (Springer-Verlag, 1982) 65-98. Zbl0501.51012
  3. [3] M. Voigt and H. Walther, Polyhedral graphs with restricted number of faces of the same type, Preprint No. M22/99, Technical University Ilmenau (submitted to Discr. Math.). Zbl0995.05039
  4. [4] H. Walther, Polyhedral graphs with extreme numbers of types of faces, Preprint No. M13/99, Technical University Ilmenau (submitted to Appl. Discr. Math.). Zbl1072.05539

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