Bipartite Graphs and Monochromatic Squares

Shimon Garti

doi:10.1007/s11083-018-9457-4

Bipartite Graphs and Monochromatic Squares

Shimon Garti

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
Externally published	Yes

Keywords

Bipartite graph
Polarized relation
Saturated ideals

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology
Computational Theory and Mathematics

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10.1007/s11083-018-9457-4

Cite this

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title = "Bipartite Graphs and Monochromatic Squares",

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.",

keywords = "Bipartite graph, Polarized relation, Saturated ideals",

author = "Shimon Garti",

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AB - 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.

KW - Bipartite graph

KW - Polarized relation

KW - Saturated ideals

UR - https://www.scopus.com/pages/publications/85044447384

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DO - 10.1007/s11083-018-9457-4

M3 - Article

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Bipartite Graphs and Monochromatic Squares

Abstract

Keywords

ASJC Scopus subject areas

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