Contraction Bidimensionality of Geometric Intersection Graphs - Baste, Julien; Thilikos, Dimitrios M. (Algorithmica, 2022)
Given a graph G , we define bcg ( G ) as the minimum k for which G can be contracted to the uniformly triangulated grid Γ k . A graph class G has the SQG C property if every graph G ∈ G has treewidth O ( bcg ( G ) c ) for some 1 ≤ c < 2 . The SQG C property is important for algorithm 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 wide family of graph classes that satisfy the SQG C property. This family includes, in particular, bounded-degree string graphs. This considerably extends the applicability of bidimensionality theory for contraction bidimensional problems.