Theorems · Theorem · combinatorics

SimpleGraph.isAcyclic_sSup_of_isAcyclic_directedOn

∀ {V : Type u_1} (Hs : Set (SimpleGraph V)),
  (∀ H ∈ Hs, H.IsAcyclic) → DirectedOn (fun x1 x2 => x1 ≤ x2) Hs → (sSup Hs).IsAcyclic

The directed supremum of acyclic graphs is acyclic.

Defined in

Mathlib.Combinatorics.SimpleGraph.Acyclic

Cited by

1 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound