## 1.5-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor (2002)

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Venue: | IN THE 5TH INTERNATIONAL WORKSHOP ON APPROXIMATION ALGORITHMS FOR COMBINATORIAL OPTIMIZATION (ITALY, APPROX 2002), LNCS, 2002 |

Citations: | 8 - 6 self |

### BibTeX

@INPROCEEDINGS{Demaine021.5-approximationfor,

author = {Erik D. Demaine and MohammadTaghi Hajiaghayi and Dimitrios M. Thilikos},

title = {1.5-Approximation for Treewidth of Graphs Excluding a Graph with One Crossing as a Minor},

booktitle = {IN THE 5TH INTERNATIONAL WORKSHOP ON APPROXIMATION ALGORITHMS FOR COMBINATORIAL OPTIMIZATION (ITALY, APPROX 2002), LNCS, 2002},

year = {2002},

pages = {67--80},

publisher = {}

}

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### 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 K5-minor- free 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.