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Distance to interval graphs

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

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    Natural Language Statement

    Definition

    The minimum number of vertices whose deletion leaves an intersection graph of nonempty closed intervals on the real line.

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    DefinitionThis conceptRelated conceptA → B: B builds on A

    Lean source view on GitHub

    1import Lax560391.IntervalGraphs
    2import Mathlib.Combinatorics.SimpleGraph.Finite
    3import Mathlib.Order.Lattice.Nat
    4
    5/-!
    6---
    7title: Distance to interval graphs
    8type: definition
    9---
    10The minimum number of vertices whose deletion leaves an intersection graph of
    11nonempty closed intervals on the real line.
    12-/
    13
    14namespace Lax560391.DistanceToInterval
    15
    16open Lax560391.IntervalGraphs
    17
    18noncomputable def distanceToInterval {V : Type} [Fintype V] [DecidableEq V]
    19 (G : SimpleGraph V) : ℕ :=
    20 sInf {k : ℕ | ∃ S : Finset V, (S.card = k) ∧
    21 (IsInterval (G.induce {v | v ∉ S}))}
    22
    23end Lax560391.DistanceToInterval
    24
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