Bipartite Graphs and Monochromatic Squares

Shimon Garti

doi:10.1007/s11083-018-9457-4

Bipartite Graphs and Monochromatic Squares

Shimon Garti^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

Abstract

Let κ be a successor cardinal. We prove that consistently every bipartite graph of size κ ⁺ × κ ⁺ contains either an independent set or a clique of size τ × τ for every ordinal τ < κ ⁺ . We prove a similar theorem for ℓ-partite graphs.

Original language	English
Pages (from-to)	99-106
Number of pages	8
Journal	Order
Volume	36
Issue number	1
DOIs	https://doi.org/10.1007/s11083-018-9457-4
State	Published - 15 Mar 2019

Bibliographical note

Publisher Copyright:
© 2018, Springer Science+Business Media B.V., part of Springer Nature.

Keywords

Bipartite graph
Polarized relation
Saturated ideals

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10.1007/s11083-018-9457-4

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KW - Bipartite graph

KW - Polarized relation

KW - Saturated ideals

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Bipartite Graphs and Monochromatic Squares

Abstract

Bibliographical note

Keywords

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