On incompactness for chromatic number of graphs

Saharon Shelah

doi:10.1007/s10474-012-0287-3

On incompactness for chromatic number of graphs

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

5 Scopus citations

Abstract

We deal with incompactness. Assume the existence of non-reflecting stationary set of cofinality κ. We prove that one can define a graph G whose chromatic number is >κ, while the chromatic number of every subgraph G′{subset double equals}G, {pipe}G′{pipe}<{pipe}G{pipe} is ≦κ. The main case is κ=א₀.

Original language	English
Pages (from-to)	363-371
Number of pages	9
Journal	Acta Mathematica Hungarica
Volume	139
Issue number	4
DOIs	https://doi.org/10.1007/s10474-012-0287-3
State	Published - Jun 2013

Keywords

03E05
05C15
chromatic number
compactness
graph
non-reflecting stationary set
set theory

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10.1007/s10474-012-0287-3

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AB - We deal with incompactness. Assume the existence of non-reflecting stationary set of cofinality κ. We prove that one can define a graph G whose chromatic number is >κ, while the chromatic number of every subgraph G′{subset double equals}G, {pipe}G′{pipe}<{pipe}G{pipe} is ≦κ. The main case is κ=א0.

KW - 03E05

KW - 05C15

KW - chromatic number

KW - compactness

KW - graph

KW - non-reflecting stationary set

KW - set theory

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JO - Acta Mathematica Hungarica

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ER -

On incompactness for chromatic number of graphs

Abstract

Keywords

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