Classes and Recognition of Curve Contact Graphs

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. Various classes of contact graphs are introduced and the inclusions between them are described, also the recognition of the contact graphs is studied. As one of the main results, it is proved that the recognition of 3-contact graphs isNP-complete for planar graphs, while the same question for planar triangulations is polynomial.