Universal Graphs with Forbidden Subgraphs and Algebraic Closure

Gregory Cherlin; Saharon Shelah; Niandong Shi

doi:10.1006/aama.1998.0641

Universal Graphs with Forbidden Subgraphs and Algebraic Closure

Gregory Cherlin^*, Saharon Shelah, Niandong Shi

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

55 Scopus citations

Abstract

We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an associated "algebraic closure" operator. The main applications are new examples of universal graphs with forbidden subgraphs and simplified treatments of some previously known cases.

Original language	English
Pages (from-to)	454-491
Number of pages	38
Journal	Advances in Applied Mathematics
Volume	22
Issue number	4
DOIs	https://doi.org/10.1006/aama.1998.0641
State	Published - May 1999

Keywords

Universal graph; forbidden subgraph; algebraic closure; model theory; א-categoricity; model completeness; existential completeness

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10.1006/aama.1998.0641

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AB - We apply model theoretic methods to the problem of existence of countable universal graphs with finitely many forbidden connected subgraphs. We show that to a large extent the question reduces to one of local finiteness of an associated "algebraic closure" operator. The main applications are new examples of universal graphs with forbidden subgraphs and simplified treatments of some previously known cases.

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Universal Graphs with Forbidden Subgraphs and Algebraic Closure

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