PPL 066 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
Prize Problem LedgerErdősPPL 066Erdős Problem #601

Permanent problem IDPPL 066

Verified openErdősconjecture

Graph theory

Erdős Problem #601

For which limit ordinals α is it true that if G is a graph with vertex set α then G must have either an infinite path or independent set on a set of vertices with order type α?

graph theoryset theory
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The problem

For which limit ordinals α is it true that if G is a graph with vertex set α then G must have either an infinite path or independent set on a set of vertices with order type α?

Open since1970exact
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