\input zb-basic
\input zb-ioport
\iteman{io-port 02142654}
\itemau{Jiang, Tao; West, Douglas B.}
\itemti{On the Erd\H os-Simonovits-S\'os conjecture about the anti-Ramsey number of a cycle.}
\itemso{Comb. Probab. Comput. 12, No. 5-6, 585-598 (2003).}
\itemab
For a positive integer $n$ and a family $\Cal F$ of graphs $f(n, \Cal F)$ denotes the maximum number of colours in an edge colouring of the complete graph $K_n$ with the property that no subgraph of $K_n$ that belongs to $\Cal F$ has distinct colours on its edges. A previously known bound for $\Cal F =\{ C_k\} $ is improved to $f(n,\{ C_k\} )\leq (\frac{k+1}{2} - \frac{2}{k-1})n - (k-2)$. For even $k$, it is further improved to $\frac{k}{2}n - (k-2)$. Furthermore, it is proved that $f(n,\{ C_k,C_{k+1},C_{k+2}\} )\leq (\frac{k-2}{2} + \frac{1}{k-1})n - 1$, which is sharp.
\itemrv{Dalibor Fron\v cek (Duluth)}
\itemcc{}
\itemut{edge colouring}
\itemli{doi:10.1017/S096354830300590X}
\end