## Abstract An exact structure is described to classify the projectiveβplanar graphs that do not contain a __K__~3, 4~βminor. Copyright Β© 2011 Wiley Periodicals, Inc. J Graph Theory
Projective-planar graphs with even duals
β Scribed by Seiya Negami
- Publisher
- John Wiley and Sons
- Year
- 1992
- Tongue
- English
- Weight
- 472 KB
- Volume
- 16
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
Let G be a connected graph which is projectiveβplanar but is not planar. It will be shown that G can be embedded in the projective plane so that it has only even faces if and only if either G is bipartite or its canonical bipartite covering is planar and that such an embedding is unique if G is 3βconnected.
π SIMILAR VOLUMES
## Abstract We give a detailed algebraic characterization of when a graph __G__ can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph __G__\* on the same edge set as __G__, which satisfies algebraic conditions inspired by homology groups and inte
A graph G is uniquelyembeddable in a surface f 2 if for any two embeddings f,,f2 : G + f 2 , there exists an isomorphism u : G + G and a homeo- admits an embedding f : G + F2 such that for any isomorphism (T : G + G, there is a homeomorphism h : F 2 f 2 with h . f = f . u. It will be shown that if
An edge or face of an embedded graph is light if the sum of the degrees of the vertices incident with it is small. This paper parallelizes four inequalities on the number of light edges and light triangles from the plane to the projective plane. Each of the four inequalities is shown to be the best
We identify the structures of 4-connected projective-planar graphs which generate their inequivalent embeddings on the projective plane, showing two series of graphs the number of whose inequivalent embeddings is held by O(n) with respect to the number of its vertices n.
We investigate the structure of the free amalgamated product P 1 \* P 1 β©P 2 P 2 in which P 1 and P 2 are isomorphic projective linear groups and P 1 β© P 2 is a one-point stabilizer in the natural action of P i on the points of a projective space of dimension n β₯ 2. We apply the results to graphs ad