GracefulLabeling.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

3 declarations, 1 contain sorry, 0 declared as axioms

Graceful Tree Conjecture (Ringel–Kotzig conjecture)

Reference: Wikipedia/Graceful_labeling

Conjectured by Ringel (1963) and Kotzig; formalized by Rosa (1967).

Imports (1)

FormalConjecturesUtil

lemma GracefulLabeling.graceful_tree_one_vertex line 35 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: SimpleGraph, Unit, Bot.bot, Nat, Finset.card, Sym2, SimpleGraph.edgeFinset, Exists, And, Function.Injective, LE.le, Eq, Finset, Finset.image, Equiv, Subtype, Sym2.lift, Subtype.mk, Int.natAbs, HSub.hSub and 3 more
Proof uses: Exists.intro, And.intro, rfl, Nat.zero_le, of_eq_true, Eq.trans, EmptyCollection.emptyCollection, True, congr, congrArg, funext, CharP.cast_eq_zero, sub_self, congrFun', Subtype.mk.congr_simp, SimpleGraph.edgeFinset_bot, Finset.Icc_eq_empty_of_lt, LT.lt, eq_self
66 instances, coercions and auxiliary constants left out.

Tactic trace: 6 steps
Open to load the checked before-and-after goal states.
lemma GracefulLabeling.graceful_tree_two_vertex line 52 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: SimpleGraph, Fin, OfNat.ofNat, Nat, Top.top, Finset.card, Sym2, SimpleGraph.edgeFinset, Exists, And, Function.Injective, LE.le, Eq, Finset, Finset.image, Equiv, Subtype, Sym2.lift, Subtype.mk, Int.natAbs and 3 more
Proof uses: Exists.intro, And.intro, Fin.val_injective, of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl
48 instances, coercions and auxiliary constants left out.

Tactic trace: 8 steps
Open to load the checked before-and-after goal states.
theorem GracefulLabeling.graceful_tree_conjecture Every tree admits a graceful labeling sorry line 77 source
Source documentation
Every tree admits a graceful labeling.
A graceful labeling of a tree $T$ with $m$ edges is an injective map $f : V \to \{0, \dots, m\}$ such that the multiset of absolute differences $|f(u) - f(v)|$ over edges $\{u,v\}$ of $T$ equals $\{1, \dots, m\}$.

depends on sorry what this means
Statement uses: Fintype, DecidableEq, SimpleGraph, DecidableRel, SimpleGraph.Adj, SimpleGraph.IsTree, Nat, Finset.card, Sym2, SimpleGraph.edgeFinset, Exists, And, Function.Injective, LE.le, Eq, Finset, Finset.image, Equiv, Subtype, Sym2.lift and 6 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
30 instances, coercions and auxiliary constants left out.

Tactic trace: 3 steps
Open to load the checked before-and-after goal states.
```
theorem graceful_tree_conjecture {V : Type*} [Fintype V] [DecidableEq V]
    (T : SimpleGraph V) [DecidableRel T.Adj] (hT : T.IsTree) :
    let m := T.edgeFinset.card
…
```