The board / graph theory / #1105
Erdős Problem #1105
PROVEDdatabase updated 2026-02-01
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).
The anti-Ramsey number \(\mathrm{AR}(n,G)\) is the maximum possible number of colours in which the edges of \(K_n\) can be coloured without creating a rainbow copy of \(G\) (i.e. one in which all edges have different colours). Let \(C_k\) be the cycle on \(k\) vertices. Is it true that \(\mathrm{AR}(n,C_k)=\left(\frac{k-2}{2}+\frac{1}{k-1}\right)n+O(1)\)? Montellano-Ballesteros and Neumann-Lara [MoNe05] gave an exact formula for \(\mathrm{AR}(n,C_k)\), which implies in particular that \(\mathrm{AR}(n,C_k)=\left(\frac{k-2}{2}+\frac{1}{k-1}\right)n+O(1).\)
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/1105.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1105
Attempts
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