PPL 079 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
Prize Problem LedgerErdősPPL 079Erdős Problem #74

Permanent problem IDPPL 079

Verified openErdősconjecture

Graph theory

Erdős Problem #74

Let f(n)→ ∈fty (possibly very slowly). Is there a graph of infinite chromatic number such that every finite subgraph on n vertices can be made bipartite by deleting at most f(n) edges?

graph theorychromatic numbercycles
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The problem

Let f(n)→ ∈fty (possibly very slowly). Is there a graph of infinite chromatic number such that every finite subgraph on n vertices can be made bipartite by deleting at most f(n) edges?

Open since1982exact
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$500Paul Erdős / Combinatorics Foundation
Documented

A solution must appear in a reputable journal, with documentation that Erdős offered the displayed amount. Claims are administered by the Combinatorics Foundation; erdosproblems.com does not pay awards.

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Sources & reading