-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor

نویسندگان

  • Erik D. Demaine
  • Mohammad Taghi Hajiaghayi
  • Dimitrios M. Thilikos
چکیده

We give polynomial-time constant-factor approximation algorithms for the treewidth and branchwidth of any H-minor-free graph for a given graph H with crossing number at most 1. The approximation factors are 1.5 for treewidth and 2.25 for branchwidth. In particular, our result directly applies to classes of nonplanar graphs such as K5-minorfree graphs and K3,3-minor-free graphs. Along the way, we present a polynomial-time algorithm to decompose H-minor-free graphs into planar graphs and graphs of treewidth at most cH (a constant dependent on H) using clique sums. This result has several applications in designing fully polynomial-time approximation schemes and fixed-parameter algorithms for many NP-complete problems on these graphs.

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تاریخ انتشار 2002