Planar Branch Decompositions II: The Cycle Method

References

• Alvarez C., Cases R., Diaz J., Petit J., Serna M. Routing tree problems on random graphs. (2000) . Technical report LSI-01-10-R, Software Department, Universitat Politecnica de Catalunya, Barcelona, SpainGoogle Scholar
• Arnborg S., Lagergren J., Seese D. Easy problems for tree-decomposable graphs. J. Algorithms (1991) 12:308–340Crossref, Google Scholar
• Boyer J., Myrvold M. Stop minding your P's and Q's: A simplified O(n) planar embedding algorithm. Tenth Annual ACM-SIAM Sympos. Dicrete Algorithms (1999) (ACM, New York) 140–146Google Scholar
• Cook W., Seymour P. Tour merging via branch-decomposition. INFORMS J. Comput. (2003) 15:233–248Link, Google Scholar
• Edelsbrunner H.Algorithms in Combinatorial Geometry (1987) (Springer-Verlag, Berlin, Germany) Crossref, Google Scholar
• Geelen J., Gerards A., Whittle G. Branch width and well-quasi-ordering in matroids and graphs. J. Comb. Theory, Series B (2002) 84:270–290Crossref, Google Scholar
• Hicks I. V.Branch Decompositions and their Applications (2000) . Ph.D. thesis, Computational and Applied Mathematics Department, Rice University, Houston, TXGoogle Scholar
• Hicks I. V. Branchwidth heuristics. Congressus Numerantium (2002) 159:31–50Google Scholar
• Hicks I. V. Branch decompositions and minor containment. Networks (2004a) 43:1–9Crossref, Google Scholar
• Hicks I. V. New facets for the planar subgraph polytope. (2004b) . Working paper, Industrial Engineering Department, Texas A&M University, College Station, TXGoogle Scholar
• Hicks I. V. Planar branch decompositions I: The ratcatcher. INFORMS J. Comput. (2005) 17:402–412Link, Google Scholar
• Liebers A. Planarizing graphs: A survey and annotated bibliography. J. Graph Algorithms Appl. (2001) 5:1–74Crossref, Google Scholar
• Reinelt G. TSPLIB—A traveling salesman library. ORSA J. Comput. (1991) 3:376–384Link, Google Scholar
• Robertson N., Seymour P. Graph minors: A survey. Survey in Combinatorics (1985) (Cambridge University Press, Cambridge, UK) 153–171Crossref, Google Scholar
• Robertson N., Seymour P. Graph minors X: Obstructions to tree-decompositions. J. Combin. Theory, Series B (1991) 52:153–190Crossref, Google Scholar
• Robertson N., Seymour P. Graph minors XIII: The disjoint paths problem. J. Combin. Theory, Series B (1995) 63:65–110Crossref, Google Scholar
• Seymour P., Thomas R. Call routing and the ratcatcher. Combinatorica (1994) 14:217–241Crossref, Google Scholar
• Tamaki H. A linear time heuristic for the branch-decomposition of planar graphs. (2003) . Technical report MPI-I-2003-1-010, Max-Planck-Institut Fur Informatick, Saarbrücken, GermanyGoogle Scholar