The board / graph theory / #81
Erdős Problem #81
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).
Let \(G\) be a chordal graph on \(n\) vertices - that is, \(G\) has no induced cycles of length greater than \(3\). Can the edges of \(G\) be partitioned into \(n^2/6+O(n)\) many cliques?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/81.Prizenone
Topicsgraph theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/81
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Live Erdős Problems #81 status is OPEN with 0 claimed proofs and “Currently working on this problem: None,” but it lists jtraverso under “I am working on formalising the results on this problem”; this
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