PPL 082 / 177 permanent IDsPrize Problem Ledger · PPLChecked 2026.07.26
Prize Problem LedgerErdősPPL 082Erdős Problem #86

Permanent problem IDPPL 082

Verified openErdősconjecture

Graph theory

Erdős Problem #86

Let Q_n be the n-dimensional hypercube graph (so that Q_n has 2^n vertices and n2^(n-1) edges). Is it true that every subgraph of Q_n with ≥ ((1/2)+o(1))n2^(n-1) many edges contains a C_4?

graph theory
01

The problem

Let Q_n be the n-dimensional hypercube graph (so that Q_n has 2^n vertices and n2^(n-1) edges). Is it true that every subgraph of Q_n with ≥ ((1/2)+o(1))n2^(n-1) many edges contains a C_4?

Open since1991source estimate
Last checked2026.07.26Catalog verification
02

Reward offers

Offer 01$100Paul 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.

03

Sources & reading