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Distance to distance-hereditary graphs

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

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    Natural Language Statement

    Definition

    The minimum number of vertices whose deletion leaves a graph in which every connected induced subgraph preserves distances.

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    2 concepts
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    DefinitionThis conceptRelated conceptA → B: B builds on A

    Lean source view on GitHub

    1import Lax560391.DistanceHereditaryGraphs
    2import Mathlib.Combinatorics.SimpleGraph.Finite
    3import Mathlib.Order.Lattice.Nat
    4
    5/-!
    6---
    7title: Distance to distance-hereditary graphs
    8type: definition
    9---
    10The minimum number of vertices whose deletion leaves a graph in which every
    11connected induced subgraph preserves distances.
    12-/
    13
    14namespace Lax560391.DistanceToDistanceHereditary
    15
    16open Lax560391.DistanceHereditaryGraphs
    17
    18noncomputable def distanceToDistanceHereditary
    19 {V : Type} [Fintype V] [DecidableEq V]
    20 (G : SimpleGraph V) : ℕ :=
    21 sInf {k : ℕ | ∃ S : Finset V, (S.card = k) ∧
    22 (IsDistanceHereditary (G.induce {v | v ∉ S}))}
    23
    24end Lax560391.DistanceToDistanceHereditary
    25
    Builds on
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    From Mathlib

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