Open Research Index

Erdős Problem 111: bipartizing finite subgraphs of uncountably chromatic graphs

Jacob Parish

Palomar Registrypalomar/PALOMAR-2026-10-19-000007Oct 19, 2026math.COscore 0

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.

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