A new approach for contact graph representations and its applications

Abstract

A contact graph representation is a classical graph drawing style in which vertices are represented by geometric objects such that edges correspond to contacts between objects. Based on a characterization of stretchable systems of pseudo segments, we present a new approach for constructing a wide range of contact graph representations. Using Courcelle’s theorem, some useful fixed-parameter tractability results are derived. Our approach can also be applied to giving quick proofs for some existing results of contact graph representations. We feel that the technique developed in the paper gives new insight to the study of contact representations of plane graphs.