Some Recent Progress and Applications in Graph Minor Theory

@article{Kawarabayashi2007SomeRP,
  title={Some Recent Progress and Applications in Graph Minor Theory},
  author={Ken-ichi Kawarabayashi and Bojan Mohar},
  journal={Graphs and Combinatorics},
  year={2007},
  volume={23},
  pages={1-46}
}
In the core of the seminal Graph Minor Theory of Robertson and Seymour lies a powerful theorem capturing the ``rough'' structure of graphs excluding a fixed minor. This result was used to prove Wagner's Conjecture that finite graphs are well-quasi-ordered under the graph minor relation. Recently, a number of beautiful results that use this structural result have appeared. Some of these along with some other recent advances on graph minors are surveyed. 

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