## Abstract Let __G__ be the unique 4βconnected simple graph obtained by adding an edge to the Octahedron. Every 4βconnected graph that does not contain a minor isomorphic to __G__ is either planar or the square of an odd cycle. Β© 2007 Wiley Periodicals, Inc. J Graph Theory 57: 124β130, 2008
An excluded minor theorem for the octahedron
β Scribed by Maharry, John
- Publisher
- John Wiley and Sons
- Year
- 1999
- Tongue
- English
- Weight
- 221 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
In this article it is shown that every 4-connected graph that does not contain a minor isomorphic to the octahedron is isomorphic to the square of an odd cycle.
π SIMILAR VOLUMES
We give a simple proof of the fact (which follows from the Robertson Seymour theory) that a graph which is minimal of genus g cannot contain a subdivision of a large grid. Combining this with the tree-width theorem and the quasi-wellordering of graphs of bounded tree-width in the Robertson Seymour t
This paper strengthens the excluded-minor characterization of GF(4)-representable matroids. In particular, it is shown that there are only finitely many 3-connected matroids that are not GF(4)-representable and that have no U 2, 6 -, U 4, 6 -, P 6 -, F & 7 -, or (F & 7 )\*-minors. Explicitly, these
## Abstract In 1890, Heawood established the upper bound $H ( \varepsilon )= \left \lfloor 7+\sqrt {24\varepsilon +1}/{2}\right \rfloor$ on the chromatic number of every graph embedded on a surface of Euler genus Ξ΅ β₯ 1. Almost 80 years later, the bound was shown to be tight by Ringel and Youngs. Th