## Abstract A wellโknown conjecture of Erdลs states that given an infinite graph __G__ and sets __A__,โโโ__V__(__G__), there exists a family of disjoint __A__โโโ__B__ paths ๐ together with an __A__โโโ__B__ separator __X__ consisting of a choice of one vertex from each path in ๐ . There is a natural
An accessibility theorem for infinite graph minors
โ Scribed by Reinhard Diestel
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 67 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
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.
## Abstract Let __G__ be the unique 4โconnected simple graph obtained by adding an edge to the Octahedron. Every 4โconnected graph that does not contain a minor isomorphic to __G__ is either planar or the square of an odd cycle. ยฉ 2007 Wiley Periodicals, Inc. J Graph Theory 57: 124โ130, 2008
In this paper w e determine the circumstances under which a set of 11 vertices in a 3-connected cubic graph lies on a cycle. In addition, w e consider the number of such cycles that exist and characterize those graphs in which a set of 9 vertices lies in exactly two cycles.