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Seminar on Reckoning

Hajnal--Máté Graphs and Cohen Reals

David Uhrik


Seminar on Reckoning
Wednesday, 22. March 2023 - 11:00 to 14:00

Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building

We will study Hajnal--Máté (HM) graphs. The first construction of an HM graph was from the diamond+ principle. Since then several other constructions were provided with additional interesting properties, e.g. having no triangles. We will survey results about this class of graphs and provide a construction of a triangle free HM graph in a model after adding a single Cohen real. Time permitting we will introduce a generalization, so-called δ-Hajnal--Máté graphs, and prove some of their basic properties and deduce a weak partition relation on ω2.