A short proof of the existence of designs

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arxiv 2411.18291 v1 pith:V37BVJLN submitted 2024-11-27 math.CO

Peter Keevash This is my paper

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keywords designsexistenceproofbetterboundsgivegivesmuch

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We give a new proof of the existence of designs, which is much shorter and gives better bounds.

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Erd\H{o}s meets Nash-Williams
math.CO 2025-07 conditional novelty 8.0 of 10

Every sufficiently large triangle-divisible graph with minimum degree at least (7+√21)/14 + epsilon has a triangle decomposition with arbitrarily large girth.