PPL 065 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
Prize Problem LedgerPPL · Open reward indexAll 177 problems
Prize Problem LedgerErdősPPL 065Erdős Problem #595

Permanent problem IDPPL 065

Verified openErdősconjecture

Graph theory

Erdős Problem #595

Is there an infinite graph G which contains no K_4 and is not the union of countably many triangle-free graphs?

graph theoryset theory
01

The problem

Is there an infinite graph G which contains no K_4 and is not the union of countably many triangle-free graphs?

Open since1970source estimate
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$250Paul 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.

Award source ↗Rules ↗
03

Sources & reading

2 unique reference linksCanonical problem page Claim or award rules
04

Related open targets

Graph theoryKrenn-Gu conjecturePPL 109 · €3,000 · 8 years openGraph theoryErdős Problem #625PPL 068 · $1000 · 37 years openGraph theoryErdős Problem #146PPL 045 · $500 · 42 years open