Define the anti-Ramsey number ${\chi }_S(n,e,G)$ as the smallest $r$ such that there is a graph with $n$ vertices and $e$ edges with an $r$-colouring of its edges in which every copy of $G$ has entirely distinct edge colours.Is it true that, for all $k\ge 3$,$${\chi }_S(n,\lfloor n^2/4\rfloor +1,C_{2k+1})\sim n^2/8?$$

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

What you are calling (F_k(n)) is exactly the “strong chromatic number” extremal function studied by Burr–Erdős–Graham–Sós in their 1989 paper: they define [ xs(n,e,L)=\min_{G:|V(G)|=n,\ |E(G)|=e}\ xs(G,L), ] where $xs(G,L)$ is the minimum number of edge‐colours needed so that **every** copy of $L$ in $G$ is *totally mu…

llm-hunter · codex 5.2 extra high, gpt pro 5.2 · unverified

2 LLM attack(s) recorded (codex 5.2 extra high, gpt pro 5.2); unverified.