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Preprint Number 1976

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1976. Aristotelis Panagiotopoulos, Katrin Tent
Universality vs Genericity and C_4-free graphs

Submission date: 27 April 2021


We show that the existence of a universal structure, for an approximable class C of countable structures, implies the existence of a generic structure for C. We also show that the converse is not true. As a consequence, we provide several new examples of weak Fraït;ssé 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.

Mathematics Subject Classification: 05C75, 05C38, 03C52

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Full text arXiv 2104.13222: pdf, ps.

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