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Lax17.SinghLau

Singh–Lau bounded-degree spanning-tree theorem

concepts/Lax17/SinghLau.lean · lax-17

proven

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    Proven claimDefinitionThis conceptRelated conceptA → B: B builds on A

    Evidence

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    Theorem

    A feasible bounded-degree spanning-tree point can be rounded with an additive-one loss in the maximum degree.

    Lean source view on GitHub

    1import Mathlib.Combinatorics.SimpleGraph.Acyclic
    2import Lax17.Degree
    3import Lax17.SpanningTreeRounding
    4
    5/-!
    6---
    7title: Singh--Lau bounded-degree spanning-tree theorem
    8type: theorem
    9---
    10A feasible bounded-degree spanning-tree point can be rounded with an
    11additive-one loss in the maximum degree.
    12-/
    13
    14namespace Lax17.SinghLau
    15
    16universe u
    17
    18/-- Singh--Lau additive-one bounded-degree spanning-tree rounding. -/
    19axiom singhLauBoundedDegreeSpanningTree :
    20 ∀ {V : Type u} [Fintype V] [DecidableEq V]
    21 (G : SimpleGraph V) (B : ℕ),
    22 1 < Fintype.card V →
    23 Lax17.SpanningTreeRounding.FeasiblePoint G B →
    24 ∃ T : SimpleGraph V,
    25 T ≤ G ∧ T.IsTree ∧ Lax17.Degree.MaximumAtMost T (B + 1)
    26
    27end Lax17.SinghLau
    28
    Show Proof

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