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arXiv · 1402.2700

Bowtie-free graphs have a Ramsey lift

Jan Hubička·Jaroslav Nešetřil
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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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Jan Hubička, Jaroslav Nešetřil. 2017-12-11. Bowtie-free graphs have a Ramsey lift. https://doi.org/10.1016/j.aam.2017.12.005

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