# 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

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top## How to cite

topAndrey 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

top- [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] B. Grünbaum and C.J. Shephard, Spherical tilings with transitivity properties, in: Geometrie (Springer-Verlag, 1982) 65-98. Zbl0501.51012
- [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] 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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