{"id":"palomar/PALOMAR-2026-10-19-000007","url":"https://github.com/plasma-ai/erdos-111/tree/de72caf0e388c729697b6813f4ea90bfe1617c7b","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-19-000007-v1.json","repo":"https://github.com/plasma-ai/erdos-111","tags":["math.CO","math.LO","msc:05C15","msc:05C63","msc:03E05","graph-theory","chromatic-number","formalization"],"score":0,"title":"Erdős Problem 111: bipartizing finite subgraphs of uncountably chromatic graphs","trust":"high","domain":"math.CO","source":"palomar","authors":["Jacob Parish"],"reviews":0,"subject":"math.CO","summary":"A Lean proof that for every real C, a graph whose finite subgraphs on m vertices can each be made bipartite by deleting at most Cm edges has countable chromatic number. Hence h_G(n)/n → ∞ for every graph G that is not countably colorable, in particular for every graph of chromatic number ℵ₁. This answers the second question of Erdős Problem 111 in the affirmative.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-19","reactions":{},"formalized":true}