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Is minimum colors needed to assign colors to edges of complete graph $K_n$ so that every even simple cycle contains an odd number ($>1$) of colors much larger than $(\log n)^\beta$ or $n^{\frac{1}\beta}$ with some fixed $\beta>1$?

What is a good upper bound?

Is minimum colors needed to assign colors to edges of complete graph $K_n$ so that every even simple cycle contains an odd number ($>1$) of colors much larger than $(\log n)^\beta$ or $n^{\frac{1}\beta}$ with some fixed $\beta>1$?

Is minimum colors needed to assign colors to edges of complete graph $K_n$ so that every even simple cycle contains an odd number ($>1$) of colors much larger than $(\log n)^\beta$ or $n^{\frac{1}\beta}$ with some fixed $\beta>1$?

What is a good upper bound?

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Turbo
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Is minimum colors needed to assign colors to edges of complete graph $K_n$ so that every even simple cycle contains an odd number ($>1$) of colors much larger than $(\log n)^\beta$ or $n^{\frac{1}\beta}$ with some fixed $\beta>1$?

Is minimum colors needed to assign colors to edges of complete graph $K_n$ so that every even simple cycle contains an odd number ($>1$) of colors much larger than $(\log n)^\beta$ with some fixed $\beta>1$?

Is minimum colors needed to assign colors to edges of complete graph $K_n$ so that every even simple cycle contains an odd number ($>1$) of colors much larger than $(\log n)^\beta$ or $n^{\frac{1}\beta}$ with some fixed $\beta>1$?

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Turbo
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What isIs minimum number of colors we needneeded to assign colors to edges of a complete graph $K_n$ so that every even simple cycle contains an odd number (bigger than $1$$>1$) of colors?

Is it much larger than $(\log n)^\beta$ with some fixed $\beta>1$?

What is minimum number of colors we need to assign colors to edges of a complete graph $K_n$ so that every even simple cycle contains an odd number (bigger than $1$) of colors?

Is it much larger than $(\log n)^\beta$ with some fixed $\beta>1$?

Is minimum colors needed to assign colors to edges of complete graph $K_n$ so that every even simple cycle contains an odd number ($>1$) of colors much larger than $(\log n)^\beta$ with some fixed $\beta>1$?

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