Dross's fractional triangle decomposition theorem #
If a finite graph has minimum degree at least nine tenths of its order, its edges admit an exact fractional decomposition into triangles. The proof peels high-degree triangles until the exact flow argument applies.
theorem
LeanPool.DrossFractionalTriangleDecomposition.dross_fractional_flow_exact
{V : Type u_1}
[Fintype V]
[DecidableEq V]
(G : SimpleGraph V)
[DecidableRel G.Adj]
(h : 9 * Fintype.card V ≤ 10 * G.minDegree)
:
Dross's theorem at the exact 9/10 minimum-degree threshold.