A graph which embeds all small graphs on any large set of vertices

S. Shelah

doi:10.1016/0168-0072(88)90052-8

A graph which embeds all small graphs on any large set of vertices

S. Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

8 Scopus citations

Abstract

For certain cardinals λ and κ a colouring P:[λ]²→λ is constructed such that if X ε{lunate}[λ]^λ and Q:[κ]²→λ, then there is a one-to-one function i:κ→X such that P(i″A)=Q(A) for every Aε{lunate}[κ]². Additional results are obtained.

Original language	English
Pages (from-to)	171-183
Number of pages	13
Journal	Annals of Pure and Applied Logic
Volume	38
Issue number	2
DOIs	https://doi.org/10.1016/0168-0072(88)90052-8
State	Published - May 1988

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title = "A graph which embeds all small graphs on any large set of vertices",

abstract = "For certain cardinals λ and κ a colouring P:[λ]2→λ is constructed such that if X ε\{lunate\}[λ]λ and Q:[κ]2→λ, then there is a one-to-one function i:κ→X such that P(i″A)=Q(A) for every Aε\{lunate\}[κ]2. Additional results are obtained.",

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AB - For certain cardinals λ and κ a colouring P:[λ]2→λ is constructed such that if X ε{lunate}[λ]λ and Q:[κ]2→λ, then there is a one-to-one function i:κ→X such that P(i″A)=Q(A) for every Aε{lunate}[κ]2. Additional results are obtained.

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A graph which embeds all small graphs on any large set of vertices

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