Bowtie-free graphs have a Ramsey lift
Abstract
A bowtie is a graph consisting of two triangles with one vertex identified. We show that the class of all (countable) 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 non-trivial Ramsey class with a non-trivial algebraic closure.
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