Large k‐preserving sets in infinite graphs

Andreas Huck; Frank Niedermeyer; Saharon Shelah

doi:10.1002/jgt.3190180411

Large k‐preserving sets in infinite graphs

Andreas Huck^*
, Frank Niedermeyer
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

Let K be a cardinal. If K χ₀, define K:= K. Otherwise, let K := K + 1. We prove a conjecture of Mader: Every infinite K‐connected graph G = (V, E) contains a set S ⊆ V with |S| = |V| such that G/S is K‐connected for all S⊆ S.

Original language	English
Pages (from-to)	413-426
Number of pages	14
Journal	Journal of Graph Theory
Volume	18
Issue number	4
DOIs	https://doi.org/10.1002/jgt.3190180411
State	Published - Jul 1994

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10.1002/jgt.3190180411

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title = "Large k‐preserving sets in infinite graphs",

abstract = "Let K be a cardinal. If K χ0, define K:= K. Otherwise, let K := K + 1. We prove a conjecture of Mader: Every infinite K‐connected graph G = (V, E) contains a set S ⊆ V with |S| = |V| such that G/S is K‐connected for all S⊆ S.",

author = "Andreas Huck and Frank Niedermeyer and Saharon Shelah",

year = "1994",

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AB - Let K be a cardinal. If K χ0, define K:= K. Otherwise, let K := K + 1. We prove a conjecture of Mader: Every infinite K‐connected graph G = (V, E) contains a set S ⊆ V with |S| = |V| such that G/S is K‐connected for all S⊆ S.

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Large k‐preserving sets in infinite graphs

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