Contact graphs are a special kind of intersection graphs of geometrical objects in which the objects are not allowed to cross but only to touch each other. Contact graphs of simple curves, and line segments as a special case, in the plane are considered. The curve contact representations are studied with respect to the maximal clique and the chromatic number of the represented graphs. All possible curve contact representations of cliques are described, and a linear bound on chromatic number in the maximal clique size is proved for the curve contact graphs.
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This work was supported by Czech research grants GAUK 193/1996 and 194/1996, GACˇR 0194/1996, and CS-US Science and Technology Research grant 94051.
