**Reference**:- Erik D. Demaine, MohammadTaghi Hajiaghayi, and Dimitrios M. Thilikos, “1.5-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor”, in
*Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2002)*, Lecture Notes in Computer Science, volume 2462, Rome, Italy, September 17–21, 2002, pages 67–80. **Abstract**:-
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*K*_{5}-minor-free graphs and*K*_{3,3}-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*c*_{H}(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. **Copyright**:- The paper is \copyright Springer-Verlag.
**Length**:- The paper is 14 pages.
**Availability**:- The paper is available in PostScript (213k) and PDF (169k).
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**Related papers**:- CliqueSum_JCSS (Approximation algorithms for classes of graphs excluding single-crossing graphs as minors)
- CliqueSum_ISAAC2002 (Exponential Speedup of Fixed-Parameter Algorithms on
*K*_{3,3}-minor-free or*K*_{5}-minor-free Graphs)

See also other papers by Erik Demaine.

Last updated October 17, 2021 by Erik Demaine.