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- W2979497063 abstract "We prove an extension of a ham sandwich theorem for families of lines in the plane by Dujmovi'{c} and Langerman. Given two sets $A, B$ of $n$ lines each in the plane, we prove that it is possible to partition the plane into $r$ convex regions such that the following holds. For each region $C$ of the partition there is a subset of $c_r n^{1/r}$ lines of $A$ whose pairwise intersections are in $C$, and the same holds for $B$. In this statement $c_r$ only depends on $r$. We also prove that the dependence on $n$ is optimal." @default.
- W2979497063 created "2019-10-18" @default.
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- W2979497063 date "2019-10-14" @default.
- W2979497063 modified "2023-09-23" @default.
- W2979497063 title "Balanced convex partitions of lines in the plane" @default.
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- W2979497063 doi "https://doi.org/10.48550/arxiv.1910.06231" @default.
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