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Universal graphs with a forbidden subgraph: Block path solidity

· 2014 · math.CO · arXiv 1404.5757

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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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Smaller universal posets

math.CO · 2025-09-22 · accept · novelty 8.0

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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  • Smaller universal posets math.CO · 2025-09-22 · accept · none · ref 17 · internal anchor

    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.