22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007) Locally Excluding a Minor Wroclaw, Poland July 10-July 14 ISBN: 0-7695-2908-9
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/LICS.2007.31
We introduce the concept of locally excluded minors. Graph classes locally excluding a minor are a common generalisation of the concept of excluded minor classes and of graph classes with bounded local tree-width. We show that first-order model-checking is fixed-parameter tractable on any class of graphs locally excluding a minor. This strictly generalises analogous results by Flum and Grohe on excluded minor classes and Frick and Grohe on classes with bounded local tree-width. As an important consequence of the proof we obtain fixed-parameter algorithms for problems such as dominating or independent set on graph classes excluding a minor, where now the parameter is the size of the dominating set and the excluded minor. We also study graph classes with excluded minors, where the minor may grow slowly with the size of the graphs and show that again, first-order model-checking is fixed-parameter tractable on any such class of graphs.
Citation:
Anuj Dawar, Martin Grohe, Stephan Kreutzer, "Locally Excluding a Minor," lics, pp.270-279, 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007), 2007 Usage of this product signifies your acceptance of the Terms of Use. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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