@article{DMGT_2002_22_1_a4,
author = {Dobrynin, Andrey and Melnikov, Leonid and Schreyer, Jens and Walther, Hansjoachim},
title = {Some news about oblique graphs},
journal = {Discussiones Mathematicae. Graph Theory},
pages = {39--50},
year = {2002},
volume = {22},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a4/}
}
TY - JOUR
AU - Dobrynin, Andrey
AU - Melnikov, Leonid
AU - Schreyer, Jens
AU - Walther, Hansjoachim
TI - Some news about oblique graphs
JO - Discussiones Mathematicae. Graph Theory
PY - 2002
SP - 39
EP - 50
VL - 22
IS - 1
UR - http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a4/
LA - en
ID - DMGT_2002_22_1_a4
ER -
%0 Journal Article
%A Dobrynin, Andrey
%A Melnikov, Leonid
%A Schreyer, Jens
%A Walther, Hansjoachim
%T Some news about oblique graphs
%J Discussiones Mathematicae. Graph Theory
%D 2002
%P 39-50
%V 22
%N 1
%U http://geodesic.mathdoc.fr/item/DMGT_2002_22_1_a4/
%G en
%F DMGT_2002_22_1_a4
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.
[1] O. Borodin, Structural properties of planar maps with the minimum degree 5, Math. Nachr. 158 (1992) 109-117, doi: 10.1002/mana.19921580108.
[2] B. Grünbaum and C.J. Shephard, Spherical tilings with transitivity properties, in: Geometrie (Springer-Verlag, 1982) 65-98.
[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.).
[4] H. Walther, Polyhedral graphs with extreme numbers of types of faces, Preprint No. M13/99, Technical University Ilmenau (submitted to Appl. Discr. Math.).
