The board / graph theory / #834
Erdős Problem #834
SOLVEDdatabase updated 2026-01-01
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Does there exist a \(3\)-critical \(3\)-uniform hypergraph in which every vertex has degree \(\geq 7\), where criticality means that the transversal number is \(3\) and deleting any edge reduces it to \(2\)? In the first formulation, the transversal notion of criticality, Li [Li25] proves that a \(3\)-critical \(3\)-uniform hypergraph must have a vertex of degree \(\leq 6\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/834.Prizenone
Topicsgraph theory, hypergraphs
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/834
Attempts
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