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COMBINATORICS
2004

On the Chromatic Number of Intersection Graphs of Convex Sets in the Plane

8 years 5 months ago
On the Chromatic Number of Intersection Graphs of Convex Sets in the Plane
Let G be the intersection graph of a finite family of convex sets obtained by translations of a fixed convex set in the plane. We show that every such graph with clique number k is (3k - 3)-degenerate. This bound is sharp. As a consequence, we derive that G is (3k - 2)-colorable. We show also that the chromatic number of every intersection graph H of a family of homothetic copies of a fixed convex set in the plane with clique number k is at most 6k - 6.
Seog-Jin Kim, Alexandr V. Kostochka, Kittikorn Nak
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2004
Where COMBINATORICS
Authors Seog-Jin Kim, Alexandr V. Kostochka, Kittikorn Nakprasit
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