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- W2950657579 abstract "Given an integer $k geq 2$, we consider the problem of computing the smallest real number $t(k)$ such that for each set $P$ of points in the plane, there exists a $t(k)$-spanner for $P$ that has chromatic number at most $k$. We prove that $t(2) = 3$, $t(3) = 2$, $t(4) = sqrt{2}$, and give upper and lower bounds on $t(k)$ for $k>4$. We also show that for any $epsilon >0$, there exists a $(1+epsilon)t(k)$-spanner for $P$ that has $O(|P|)$ edges and chromatic number at most $k$. Finally, we consider an on-line variant of the problem where the points of $P$ are given one after another, and the color of a point must be assigned at the moment the point is given. In this setting, we prove that $t(2) = 3$, $t(3) = 1+ sqrt{3}$, $t(4) = 1+ sqrt{2}$, and give upper and lower bounds on $t(k)$ for $k>4$." @default.
- W2950657579 created "2019-06-27" @default.
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- W2950657579 date "2007-11-01" @default.
- W2950657579 modified "2023-09-27" @default.
- W2950657579 title "Geometric Spanners With Small Chromatic Number" @default.
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