Universality vs Genericity and $C_4$-free graphs

Aristotelis Panagiotopoulos; Katrin Tent

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arxiv 2104.13222 v2 pith:2YRQWIY4 submitted 2021-04-27 math.LO math.CO

Universality vs Genericity and C₄-free graphs

Aristotelis Panagiotopoulos , Katrin Tent This is my paper

classification math.LO math.CO

keywords graphsstructureclasscountableexistencefreegenericapproximable

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We show that the existence of a universal structure implies the existence of a generic structure for any approximable class $\mathcal{C}$ 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 $C_4$-free graphs does not contain a generic structure, strengthening a result of A. Hajnal and J. Pach.

Universality vs Genericity and C₄-free graphs

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