{"id":"palomar/PALOMAR-2026-10-22-000004","url":"https://github.com/sangiloum/t-perfect-graph-50/tree/6301e85869f500458f9ca8cbf76391aab238fea5","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-22-000004-v1.json","repo":"https://github.com/sangiloum/t-perfect-graph-50","tags":["math.CO","msc:05C15","msc:05C17","graph-theory","graph-coloring","formal-verification","lean"],"score":0,"title":"The 50-color theorem for t-perfect graphs","trust":"high","domain":"math.CO","source":"palomar","authors":["Sang-il Oum"],"reviews":0,"subject":"math.CO","summary":"A Lean proof that every finite t-perfect graph is 50-colorable. Here t-perfection means equality between the stable set polytope and the polytope described by coordinate, edge, and odd-cycle inequalities.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-22","reactions":{},"formalized":true,"formalizes":[{"title":"Every t-perfect graph is 50-colorable","identifier":"https://github.com/sangiloum/t-perfect-graph-50/blob/a709f257cd4687a327260f25b50da25a031cc05f/paper/main.pdf","relationship":"formalizes"},{"title":"Colouring t-perfect graphs","identifier":"arXiv:2412.17735","relationship":"adapts"},{"title":"Coloring t-perfect graphs with fewer colors","identifier":"arXiv:2607.05961","relationship":"adapts"}]}