A consistent edge partition theorem for infinite graphs
✍ Scribed by P. Komjáth; S. Shelah
- Publisher
- Akadmiai Kiad
- Year
- 1993
- Tongue
- English
- Weight
- 316 KB
- Volume
- 61
- Category
- Article
- ISSN
- 1588-2632
No coin nor oath required. For personal study only.
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## Abstract Let __G__ be an undirected graph without multiple edges and with a loop at every vertex—the set of edges of __G__ corresponds to a reflexive and symmetric binary relation on its set of vertices. Then __every edge‐preserving map of the set of vertices of G to itself fixes an edge__ [{__f
## Abstract A well‐known conjecture of Erdős states that given an infinite graph __G__ and sets __A__, ⊆ __V__(__G__), there exists a family of disjoint __A__ − __B__ paths 𝓅 together with an __A__ − __B__ separator __X__ consisting of a choice of one vertex from each path in 𝓅. There is a natural