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Distance to block graphs

Lax560391.DistanceToBlock · concepts/Lax560391/DistanceToBlock.lean · lax-560391

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    Natural Language Statement

    Definition

    The minimum number of vertices whose deletion leaves a block graph, expressed as a chordal graph with no induced diamond.

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    DefinitionThis conceptRelated conceptA → B: B builds on A

    Lean source view on GitHub

    1import Lax560391.BlockGraphs
    2import Mathlib.Combinatorics.SimpleGraph.Finite
    3import Mathlib.Order.Lattice.Nat
    4
    5/-!
    6---
    7title: Distance to block graphs
    8type: definition
    9---
    10The minimum number of vertices whose deletion leaves a block graph, expressed
    11as a chordal graph with no induced diamond.
    12-/
    13
    14namespace Lax560391.DistanceToBlock
    15
    16open Lax560391.BlockGraphs
    17
    18noncomputable def distanceToBlock {V : Type} [Fintype V] [DecidableEq V]
    19 (G : SimpleGraph V) : ℕ :=
    20 sInf {k : ℕ | ∃ S : Finset V, (S.card = k) ∧
    21 (IsBlock (G.induce {v | v ∉ S}))}
    22
    23end Lax560391.DistanceToBlock
    24
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