{"id":"palomar/PALOMAR-2026-10-09-000006","url":"https://github.com/Asad-Shahab/erdos-809-lean/tree/15f8839e2a21f64fc5558714506ebba465926eda","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-09-000006-v1.json","repo":"https://github.com/Asad-Shahab/erdos-809-lean","tags":["math.CO","msc:05C35","msc:05C15","msc:05D10","extremal-graph-theory","erdos-problems","edge-coloring"],"score":0,"title":"Erdős Problem 809: an independent proof of the seven-cycle threshold","trust":"high","domain":"math.CO","source":"palomar","authors":["Asad Shahab"],"reviews":0,"subject":"math.CO","summary":"For every fixed integer k >= 3, the minimum number of colors in an edge-coloring of an n-vertex simple graph with at least floor(n^2/4)+1 edges, in which every copy of C_(2k+1) is rainbow, is (1/8 + o(1))n^2. The minimum is attained. The development combines Asad Shahab's seven-cycle proof, using an exact rational five-vertex certificate, with a formalization of the Bucić-Chen-Ma argument for longer odd cycles.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-09","reactions":{},"formalized":true,"formalizes":[{"title":"The Burr-Erdős-Graham-Sós conjecture for the seven-cycle","identifier":"arXiv:2609.38286v1","relationship":"formalizes"},{"title":"On a maximal anti-Ramsey conjecture of Burr, Erdős, Graham, and Sós","identifier":"arXiv:2603.18952v1","relationship":"formalizes"}]}