Universal graphs with a forbidden subtree

Gregory Cherlin; Saharon Shelah

doi:10.1016/j.jctb.2006.05.008

Universal graphs with a forbidden subtree

Gregory Cherlin^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

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

10 Scopus citations

Abstract

We show that the problem of the existence of universal graphs with specified forbidden subgraphs can be systematically reduced to certain critical cases by a simple pruning technique which simplifies the underlying structure of the forbidden graphs, viewed as trees of blocks. As an application, we characterize the trees T for which a universal countable T-free graph exists.

Original language	English
Pages (from-to)	293-333
Number of pages	41
Journal	Journal of Combinatorial Theory. Series B
Volume	97
Issue number	3
DOIs	https://doi.org/10.1016/j.jctb.2006.05.008
State	Published - May 2007

Keywords

Forbidden subgraph
Graph
Model theory
Tree
Universal graph

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10.1016/j.jctb.2006.05.008

Cite this

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KW - Model theory

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Universal graphs with a forbidden subtree

Abstract

Keywords

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