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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2014
- DOI:
- 10.48550/arXiv.1402.2700
- arXiv:
- arXiv:1402.2700
- Bibcode:
- 2014arXiv1402.2700H
- Keywords:
-
- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics;
- 05C55;
- 05C15;
- 05D10;
- 03C35;
- G.2.1;
- G.2.2
- E-Print:
- 32 pages, 5 figures. Minor corrections