The board / graph theory / #584
Erdős Problem #584
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Prizenone
Topicsgraph theory, cycles
Statement in Leannot yet
Solution in Leanno
Original pageerdosproblems.com/584
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The literal live H2 assertion is false, rigorously modulo LUW Proposition 2.1: explicit D(5,q) graphs have girth at least 10 but require Omega(q^2) H2 edges; this does not settle the sparsity-qualifie
PROVED