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A minimax theorem for infinite graphs with ideal points

✍ Scribed by Norbert Polat

Publisher
Elsevier Science
Year
1992
Tongue
English
Weight
617 KB
Volume
103
Category
Article
ISSN
0012-365X

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✦ Synopsis

Polat, N., A minimax theorem for infinite graphs with ideal points, Discrete Mathematics 103 (1992) 57-65. Let d be a family of sets of ends of an infinite graph, having the property that every element of any member of 1 can be separated from the union of all other members by a finite set of vertices. By defining appropriate concepts of .&paths and of &-separators, we show that there are a set of pairwise disjoint d-paths and an &separator which have the same 'cardinality'.

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## Abstract A well‐known conjecture of ErdΕ‘s states that given an infinite graph __G__ and sets __A__,β€‰βŠ†β€‰__V__(__G__), there exists a family of disjoint __A__β€‰βˆ’β€‰__B__ paths 𝓅 together with an __A__β€‰βˆ’β€‰__B__ separator __X__ consisting of a choice of one vertex from each path in 𝓅. There is a natural