Unavoidable vertex-minors in large prime graphs
arXiv:1306.3066 · doi:10.1016/j.ejc.2014.03.013
Abstract
A graph is prime (with respect to the split decomposition) if its vertex set does not admit a partition (A,B) (called a split) with |A|, |B| >= 2 such that the set of edges joining A and B induces a complete bipartite graph. We prove that for each n, there exists N such that every prime graph on at least N vertices contains a vertex-minor isomorphic to either a cycle of length n or a graph consisting of two disjoint cliques of size n joined by a matching.
43 pages, 12 figures
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