Graph Minors

For a given graph G and integers b, f ≥ 0, let S be a subset of vertices of G of size b + 1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every graph on n vertices contains at most n/ b+f b such vertex subsets. This result from extremal combinatorics appears to be very useful in the design of several enumeration and exact algorithms. This significantly improves previous algorithms for these problems. Binary matroid minors.

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