The Inducibility of Graphs on Four Vertices

Details The Inducibility of Graphs on Four Vertices The Inducibility of Graphs on Four Vertices

2011-09-07

arxiv.org/abs/1109.1592v1

Mathematics

Combinatorics

12 pages

Scientific paper

We consider the problem of determining the maximum induced density of a graph H in any graph on n vertices. The limit of this density as n tends to infinity is called the inducibility of H. The exact value of this quantity is known only for a handful of small graphs and a specific set of complete multipartite graphs. Answering questions of [BS94] and [Exo86] we determine the inducibility of K_{1,1,2} and the paw graph. The proof is obtained using semi-definite programming techniques based on a modern language of extremal graph theory, which we develop in full detail in an accessible setting.

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