Bowtie-free graphs have a Ramsey lift
Combinatorics
2021-02-24 v5 Discrete Mathematics
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.
Keywords
Cite
@article{arxiv.1402.2700,
title = {Bowtie-free graphs have a Ramsey lift},
author = {Jan Hubička and Jaroslav Nešetřil},
journal= {arXiv preprint arXiv:1402.2700},
year = {2021}
}
Comments
32 pages, 5 figures. Minor corrections; reformatted to elsarticle; accepted to Advances in Applied Mathematics