Mathlib Map

Theorems · Theorem · combinatorics

SimpleGraph.IsTree.isAcyclic

∀ {V : Type u_1} {G : SimpleGraph V}, G.IsTree → G.IsAcyclic

A tree is acyclic.

Defined in
Mathlib.Combinatorics.SimpleGraph.Acyclic
Cited by
5 results in Mathlib
Foundations
Depth 4 from the axioms · uses no axioms
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.IsTree.colorable_two · cited by 1IsTree.colorable_twoSimpleGraph.Connected.maximal_le_isAcyclic_iff_isTree · cited by 1Connected.maximal_le_isAc…SimpleGraph.IsTree.dist_ne_of_adj · cited by 0IsTree.dist_ne_of_adjSimpleGraph.IsTree.exists_ne_and_degree_eq_one · cited by 0IsTree.exists_ne_and_degr…SimpleGraph.IsTree.IsAcyclic · cited by 0IsTree.IsAcyclicSimpleGraph · cited by 3072SimpleGraphSimpleGraph.IsAcyclic · cited by 67SimpleGraph.IsAcyclicSimpleGraph.IsTree · cited by 32SimpleGraph.IsTreeIsTree.isAcyclicCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by5

Results whose statement or proof uses this declaration.