Claims

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1966_01_01_erdos_goodman_posa: Erdős, Goodman and Pósa (1966) prove that every graph on n vertices is the union of at most floor(n^2/4) pairwise edge-disjoint edges and triangles, the case r = 2 of the Erdős–Sauer question for every n; refereed.

2026_09_07_zeraoulia: Rafik Zeraoulia's September 2026 preprint states that the Erdős–Sauer decomposition bound holds for every 3-uniform hypergraph on at most nine vertices and gives local packing lemmas; AI-assisted, not refereed, unreviewed.

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