Colouring Arcwise Connected Sets in the Plane II |
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Authors: | Sean McGuinness |
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Institution: | Department of Mathematics, Ume? University, S-90187 Ume?, Sweden, SE
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Abstract: | Let ? be the family of finite collections ? where ? is a collection of bounded, arcwise connected sets in ℝ2 where for any S,T∈? such that S∩T≠?, it holds that S∩T is arcwise connected. Given ? is triangle-free, and provided the chromatic number χ(G) of the intersection graph G=G(?) of ? is sufficiently large, there exists α>1 independent of ? such that there is a subcollection ?′⊂? of at most 5 sets with the property that the sets of ? surrounded by ?′ induce an intersection graph H where .
Received: November 13, 1995 Final version received: December 3, 1998 |
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