Universal graphs with a forbidden subgraph: Block path solidity

Gregory Cherlin; Saharon Shelah

Universal graphs with a forbidden subgraph: Block path solidity

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arxiv 1404.5757 v1 pith:XNBOBMBP submitted 2014-04-23 math.CO

Gregory Cherlin , Saharon Shelah This is my paper · ORCID

classification math.CO

keywords graphblocksc-freeconnectedcountablefinitegraphspath

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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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Smaller universal posets
math.CO 2025-09 accept novelty 8.0 of 10

Every n-element poset embeds into a poset of size at most 2^(2n/3 + C*sqrt(n)), improving the folklore 2^n upper bound for universal posets.

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