Some news about oblique graphs

• Autorzy: Andrey A. Dobrynin , Leonid S. Melnikov , Jens Schreyer , Hansjoachim Walther
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2002
• Tom: 22
• Numer: 1
• Strony: 39-50

Daty

wydano

2002

otrzymano

2001-01-29

poprawiono

2001-08-01

Twórcy

autor

Andrey A. Dobrynin

• Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Novosibirsk 630090, Russia

autor

Leonid S. Melnikov

• Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Novosibirsk 630090, Russia

autor

Jens Schreyer

• Technische Universität Ilmenau, Germany

autor

Hansjoachim Walther

• Technische Universität Ilmenau, Germany

Bibliografia

• [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.).

Identyfikatory

DOI

10.7151/dmgt.1157