Universal graphs with a forbidden subgraph: Block path solidity

Gregory Cherlin; Saharon Shelah

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arXiv · 1404.5757

Universal graphs with a forbidden subgraph: Block path solidity

Gregory Cherlin·Saharon Shelah

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Abstract

Let C be a finite connected graph for which there is a countable universal C-free graph, and whose tree of blocks is a path. Then the blocks of C are complete. This generalizes a result of Furedi and Komjath, and fits naturally into a set of conjectures regarding the existence of countable C-free graphs, with C an arbitrary finite connected graph.

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Gregory Cherlin, Saharon Shelah. 2014-04-23. Universal graphs with a forbidden subgraph: Block path solidity. https://arxiv.org/abs/1404.5757

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