Universal graphs with a forbidden subtree

Gregory Cherlin; Saharon Shelah

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arXiv · math/0512218

Universal graphs with a forbidden subtree

Gregory Cherlin·Saharon Shelah

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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.

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Gregory Cherlin, Saharon Shelah. 2005-12-10. Universal graphs with a forbidden subtree. https://arxiv.org/abs/math/0512218

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