Bidimensional Parameters and Local Treewidth

For several graph-theoretic parameters such as vertex cover and dominating set, it is known that if their sizes are bounded by k then the treewidth of the graph is bounded by some function of k. This fact is used as the main tool for the design of several fixed-parameter algorithms on minor-closed graph classes such as planar graphs, single-crossing-minor-free graphs, and graphs of bounded genus. In this paper we examine the question whether similar bounds can be obtained for larger minor-closed graph classes, and for general families of graph parameters including all those for which such behavior has been reported so far. Given a graph parameter P , we say that a graph family F has the parameter-treewidth property for P if there is an increasing function t such that every graph G ∈ F has treewidth at most t(P (G)). We prove as our main result that, for a large family of graph parameters called contraction-bidimensional, a minor-closed graph family F has the parameter-treewidth prop...

• Type: Conference
• Year: 2004
• Where: LATIN
• Authors: Erik D. Demaine, Fedor V. Fomin, Mohammad Taghi Hajiaghayi, Dimitrios M. Thilikos
• Keywords: Graph Parameters, Information Retrieval, LATIN 2004, Minor-closed Graph, Minor-closed Graph Classes