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Bowtie-free graphs have a Ramsey lift

Publication at Faculty of Mathematics and Physics |
2018

Abstract

A bowtie is a graph consisting of two triangles with one vertex identified. We show that the class of all (finite) graphs not containing a bowtie as a subgraph has a Ramsey lift (expansion).

This solves one of the old problems in the area and it is the first Ramsey class with a non-trivial algebraic closure.