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Bipartite Graphs and Monochromatic Squares

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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 -partite graphs.

Keywords

Bipartite graph Polarized relation Saturated ideals 

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

Authors and Affiliations

  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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