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Universal graphs with a forbidden subtree
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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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Smaller universal posets
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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