Abstract
Minor containment is a fundamental problem in Algorithmic Graph Theory, as numerous graph algorithms use it as a subroutine. A model of a graph H in a graph G is a set of disjoint connected subgraphs of G indexed by the vertices of H, such that if {u,v} is an edge of H, then there is an edge of G between components C u and C v . Graph H is a minor of G if G contains a model of H as a subgraph. We give an algorithm that, given a planar n-vertex graph G and an h-vertex graph H, either finds in time \(2^{\mathcal{O}(h)} \cdot n + \mathcal{O}(n^{2}\cdot \log n)\) a model of H in G, or correctly concludes that G does not contain H as a minor. Our algorithm is the first single-exponential algorithm for this problem and improves all previous minor testing algorithms in planar graphs. Our technique is based on a novel approach called partially embedded dynamic programming.
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Adler, I., Dorn, F., Fomin, F.V., Sau, I., Thilikos, D.M. (2010). Fast Minor Testing in Planar Graphs. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_9
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