The board / graph theory / #767
Erdős Problem #767
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
`G` contains a cycle with `k` chords incident to a vertex on the cycle.
`g k n` is the maximal number of edges possible on a graph with `n` vertices which does not contain a cycle with `k` chords incident to a vertex on the cycle.
Let \(g_k(n)\) be the maximal number of edges possible on a graph with \(n\) vertices which does not contain a cycle with \(k\) chords incident to a vertex on the cycle. Is it true that \[g_k(n)=(k+1)n-(k+1)^2\] for \(n\) sufficiently large? The answer is yes: the conjectured equality was proved for \(n\geq 3k+3\) by Jiang [Ji04].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/767.Prizenone
Topicsgraph theory, turan number
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/767
Attempts
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