On the Chromatic Number of Intersection Graphs of Convex Sets in the Plane
نویسندگان
چکیده
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.
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عنوان ژورنال:
- Electr. J. Comb.
دوره 11 شماره
صفحات -
تاریخ انتشار 2004