## Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring (2005)

Venue: | In 46th Annual IEEE Symposium on Foundations of Computer Science |

Citations: | 43 - 12 self |

### BibTeX

@INPROCEEDINGS{Demaine05algorithmicgraph,

author = {Erik D. Demaine and Mohammadtaghi Hajiaghayi and Ken-ichi Kawarabayashi},

title = {Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring},

booktitle = {In 46th Annual IEEE Symposium on Foundations of Computer Science},

year = {2005},

pages = {637--646},

publisher = {Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

At the core of the seminal Graph Minor Theory of Robertson and Seymour is a powerful structural theorem capturing the structure of graphs excluding a fixed minor. This result is used throughout graph theory and graph algorithms, but is existential. We develop a polynomialtime algorithm using topological graph theory to decompose a graph into the structure guaranteed by the theorem: a clique-sum of pieces almost-embeddable into boundedgenus surfaces. This result has many applications. In particular, we show applications to developing many approximation algorithms, including a 2-approximation to graph coloring, constant-factor approximations to treewidth and the largest grid minor, combinatorial polylogarithmicapproximation to half-integral multicommodity flow, subexponential fixed-parameter algorithms, and PTASs for many minimization and maximization problems, on graphs excluding a fixed minor. 1.