Approximate distance oracles for geometric graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A short list color proof of Grötzsch's theorem
Journal of Combinatorial Theory Series B
Computational Geometry: Theory and Applications - Special issue on the 14th Canadian conference on computational geometry — CCCG02
Design and evaluation of a new MAC protocol for long-distance 802.11 mesh networks
Proceedings of the 11th annual international conference on Mobile computing and networking
Geometric Spanner Networks
Proceedings of the twenty-ninth annual symposium on Computational geometry
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Given an integer k=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)=2, and give upper and lower bounds on t(k) for k4. We also show that for any @e0, there exists a (1+@e)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+3, t(4)=1+2, and give upper and lower bounds on t(k) for k4.