/-
Copyright 2026 The Formal Conjectures Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
https://www.apache.org/licenses/LICENSE-2.0
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distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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-/
module
public import Mathlib.Algebra.Ring.Parity
public import Mathlib.Combinatorics.SimpleGraph.Paths
public import Mathlib.Order.Lattice.Nat@[expose] public sectionCycle lengths and circumference
The cycle lengths and the longest cycle length of a graph.
namespace SimpleGraph
G.cycleLengths is the set of lengths of the cycles in G.
def cycleLengths {α : Type*} (G : SimpleGraph α) : Set ℕ :=
{m | ∃ (a : α) (w : G.Walk a a), w.IsCycle ∧ w.length = m}
G.oddCycleLengths is the set of lengths of odd cycles in G.
def oddCycleLengths {α : Type*} (G : SimpleGraph α) : Set ℕ :=
{m ∈ G.cycleLengths | Odd m}variable {α : Type*} [Fintype α] [DecidableEq α]
circumference G is the length of the longest cycle in G.
It is 0 when G is acyclic.
noncomputable def circumference (G : SimpleGraph α) [DecidableRel G.Adj] : ℕ :=
sSup G.cycleLengthsend SimpleGraph