Papers › Some exact inducibility-type results for graphs via flag algebras
Some exact inducibility-type results for graphs via flag algebras
Levente Bodnár, Oleg Pikhurko
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The (κ,ℓ)-edge-inducibility problem asks for the maximum number of κ-subsets inducing exactly ℓ edges that a graph of given order n can have. Using flag algebras and stability approach, we resolve this problem for all sufficiently large n (including a description of all extremal and almost extremal graphs) in eleven new non-trivial cases when κ≤7. We also compute the F-inducibility constant (the asymptotically maximum density of induced copies of F in a graph of given order n) and obtain some corresponding structure results for three new graphs F with $5$ vertices: the 3-edge star plus an isolated vertex, the 4-cycle plus an isolated vertex, and the 4-cycle with a pendant edge.
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