Planar Turán number of the 7-cycle

The planar Turán number exP(n,H) of a graph H is the maximum number of edges in an n-vertex planar graph without H as a subgraph. Let Cℓ denote the cycle of length ℓ. The planar Turán number exP(n,Cℓ) is known when ℓ∈{3,4,5,6}, and is expected to behave differently when ℓ≥11. We prove that [Formula presented] for all n≥39, and show that equality holds for infinitely many integers n.

Duke Scholars

Author Ruilin Shi Mathematics