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Andrew Ryzhikov
Andrew Ryzhikov
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Consider the following problem: given a finite set $S$ of intervals on the line and a number $k$. We need to colour this set in $k$ colours so that the measure of the set of points, which are contained in two or more intervals coloured with the same colour, is minimal for given $k$. By colouring a set $S$ in $k$ colours I mean a map from $S$ to $\{1, 2,\ldots, k\}$.

I wonder, if there are any papers on this problem or related problems.

Consider the following problem: given a set of intervals on the line and a number $k$. We need to colour this set in $k$ colours so that the measure of the set of points, which are contained in two or more intervals coloured with the same colour, is minimal for given $k$.

I wonder, if there are any papers on this problem or related problems.

Consider the following problem: given a finite set $S$ of intervals on the line and a number $k$. We need to colour this set in $k$ colours so that the measure of the set of points, which are contained in two or more intervals coloured with the same colour, is minimal for given $k$. By colouring a set $S$ in $k$ colours I mean a map from $S$ to $\{1, 2,\ldots, k\}$.

I wonder, if there are any papers on this problem or related problems.

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Andrew Ryzhikov
Andrew Ryzhikov
  • 181
  • 4

Minimize the length of intersection of the set of intervals

Consider the following problem: given a set of intervals on the line and a number $k$. We need to colour this set in $k$ colours so that the measure of the set of points, which are contained in two or more intervals coloured with the same colour, is minimal for given $k$.

I wonder, if there are any papers on this problem or related problems.