Universality vs Genericity and $C_4$-free graphs
Logic
2022-06-23 v2 Combinatorics
Abstract
We show that the existence of a universal structure implies the existence of a generic structure for any approximable class of countable structures. We also show that the converse is not true. As a consequence, we provide several new examples of weak Fra\"iss\'e classes of finite graphs. Finally, we show that the class of all countable -free graphs does not contain a generic structure, strengthening a result of A. Hajnal and J. Pach.
Keywords
Cite
@article{arxiv.2104.13222,
title = {Universality vs Genericity and $C_4$-free graphs},
author = {Aristotelis Panagiotopoulos and Katrin Tent},
journal= {arXiv preprint arXiv:2104.13222},
year = {2022}
}