|TEX2HTML_WRAP_INLINE$^$, András Gyárfás and Miklós Ruszinkó, Department of Mathematics and Computer Science, Technical University of Eindhoven; Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee 38152, USA; Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary and Computer and Automation Research Institute, Hungarian Academy of Sciences, Budapest, Hungary|
|Anti-Ramsey colorings in several rounds|
For positive integers and t let denote the minimum number of colors such that at least in one of the tcolorings of edges of Kn all edges of every get different colors. Generalizing a result of Körner and Simonyi, it is shown in this paper that . Also two-round colorings in cases k>3 are investigated. Tight bounds for for all values of k except for k=5 are obtained. Conversely, let t(k,n) denote the minimum number of colorings such that--having the same colors in each coloring--at least in one of the total t colorings of Kn all edges of every get different colors. It is also shown, that for k=n/2t(k,n) is exponentially large. Several related questions are investigated.