# On the Erdos-Simonovits-So's Conjecture about the Anti-Ramsey Number of a Cycle

@article{Jiang2003OnTE,
title={On the Erdos-Simonovits-So's Conjecture about the Anti-Ramsey Number of a Cycle},
author={Tao Jiang and Douglas B. West},
journal={Combinatorics, Probability & Computing},
year={2003},
volume={12},
pages={585-598}
}
Given a positive integer $n$ and a family ${\cal F}$ of graphs, let $f(n,{\cal F})$ denote the maximum number of colours in an edge-colouring of $K_n$ such that no subgraph of $K_n$ belonging to ${\cal F}$ has distinct colours on its edges. Erdos, Simonovits and Sos [6] conjectured for fixed $k$ with $k\geq3$ that $f(n,C_k)\,{=}\, (\frac{k-2}{2}+\frac{1}{k-1})n + O(1)$. This has been proved for $k\leq7$. For general $k$, in this paper we improve the previous bound of \$(k-2)n-\big({{k\,{-}\,1… CONTINUE READING

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