A Simple Algorithm for the Graph Minor Decomposition - Logic meets Structural Graph Theory

@inproceedings{Grohe2013ASA,
  title={A Simple Algorithm for the Graph Minor Decomposition - Logic meets Structural Graph Theory},
  author={Martin Grohe and Ken-ichi Kawarabayashi and Bruce A. Reed},
  booktitle={SODA},
  year={2013}
}
A key result of Robertson and Seymour's graph minor theory is a structure theorem stating that all graphs excluding some fixed graph as a minor have a tree decomposition into pieces that are almost embeddable in a fixed surface. Most algorithmic applications of graph minor theory rely on an algorithmic version of this result. However, the known algorithms for computing such graph minor decompositions heavily rely on the very long and complicated proofs of the existence of such decompositions… 

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