View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Dagstuhl Research Online Publication Server Contraction-Bidimensionality of Geometric Intersection Graphs∗ Julien Baste1 and Dimitrios M. Thilikos2 1 Université de Montpellier, LIRMM, Montpellier, France
[email protected] 2 AlGCo project team, CNRS, LIRMM, Montpellier, France and Department of Mathematics, National and Kapodistrian University of Athens, Greece
[email protected] Abstract Given a graph G, we define bcg(G) as the minimum k for which G can be contracted to the uniformly triangulated grid Γk. A graph class G has the SQGC property if every graph G ∈ G has treewidth O(bcg(G)c) for some 1 ≤ c < 2. The SQGC property is important for algo- rithm design as it defines the applicability horizon of a series of meta-algorithmic results, in the framework of bidimensionality theory, related to fast parameterized algorithms, kernelization, and approximation schemes. These results apply to a wide family of problems, namely problems that are contraction-bidimensional. Our main combinatorial result reveals a general family of graph classes that satisfy the SQGC property and includes bounded-degree string graphs. This considerably extends the applicability of bidimensionality theory for several intersection graph classes of 2-dimensional geometrical objects. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorithms and Problems, G.2.2 Graph Theory Keywords and phrases Grid exlusion theorem, Bidimensionality, Geometric intersection graphs, String Graphs Digital Object Identifier 10.4230/LIPIcs.IPEC.2017.5 1 Introduction Treewidth is one of most well-studied parameters in graph algorithms. It serves as a measure of how close a graph is to the topological structure of a tree (see Section 2 for the formal definition).