The Simultaneous Representation Problem for Chordal, Comparability and Permutation Graphs

Abstract. We introduce the simultaneous representation problem, defined for any graph class C characterized in terms of representations, e.g. any class of intersection graphs. Two graphs G1 and G2, sharing some vertices X (and the corresponding induced edges), are said to have a simultaneous representation with respect to a graph class C, if there exist representations R1 and R2 of G1 and G2 that are “consistent” on X. Equivalently (for the classes C that we consider) there exist edges E between G1 − X and G2 − X such that G1 ∪ G2 ∪ E belongs to class C. Simultaneous representation problems are related to graph sandwich problems, probe graph recognition problems and simultaneous planar embeddings and have applications in any situation where it is desirable to consistently represent two related graphs. In this paper we give efficient algorithms for the simultaneous representation problem on chordal, comparability and permutation graphs. These results complement the recent p...

• Type: Conference
• Year: 2009
• Where: WADS
• Authors: Krishnam Raju Jampani, Anna Lubiw
• Keywords: Algorithms, Graph Class, Graph Sandwich Problem, Simultaneous Representation Problem, WADS 2009