FormalConjecturesForMathlib.Combinatorics.SimpleGraph.Balanced

/-
Copyright 2025 The Formal Conjectures Authors.

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you may not use this file except in compliance with the License.
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module

public import Mathlib.Combinatorics.SimpleGraph.Finite
public import Mathlib.Data.Real.Basic

@[expose] public section

D-Balanced graphs

SimpleGraph.IsBalanced G D is the condition that the maximum degree of a simple graph $G$ is at most $D$ times the minimum degree.

open Fintypenamespace SimpleGraphvariable {V : Type*} [Fintype V]

We call a graph $D$-balanced (or $D$-almost-regular) if the maximum degree is at most $D$ times the minimum degree.

def IsBalanced (G : SimpleGraph V) (D : ℝ) [DecidableRel G.Adj] : Prop :=
    G.maxDegree <= D * G.minDegree

end SimpleGraph