Proof of the High Girth Existence Conjecture via Refined Absorption

Luke Postle; Michelle Delcourt

Proof of the High Girth Existence Conjecture via Refined Absorption

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arxiv 2402.17856 v1 pith:VFS73DZY submitted 2024-02-27 math.CO

Michelle Delcourt , Luke Postle This is my paper

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keywords conjectureexistencegirthhighabsorptioncombinatorialcommondesigns

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We prove the High Girth Existence Conjecture - the common generalization of the Existence Conjecture for Combinatorial Designs originating from the 1800s and Erd\H{o}s' Conjecture from 1973 on the Existence of High Girth Steiner Triple Systems.

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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.

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