Let $R_{k} (G)$ denote the minimal $m$ such that if the edges of $K_{m}$ are $k$ -coloured then there is a monochromatic copy of $G$ . Determine the value of $R_{k} (C_{2 n}) .$

Worked, still open.

graph theory · open · 0 attempts

use this record

vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Write (R_k(G):=R(G;k)) for the $k$-colour Ramsey number. For even cycles (C_{2n}), the **exact value is only known in a few cases**; in general it is an open problem.

candidate solution ↗

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

candidate solution ↗

oeis

A389313 — a(n) is the smallest m such that for every red-blue edge-coloring of the graph K_{m} there exists either a red or a blue n-cycle; Ramsey number r(C_n, C_n).6,6,9,8,13,11,17,14,21,17,25,20,29,23,33,26,37,29,41,32,45,35,49,38,53,41,57,44,61,47,65,50,69,53,73,56,77,59,81,62,85,6

links

#24 in Ramsey Theory · link

Create a formalisation here · link

status

open

evidence

oeis

links

status

Search Vela