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Distance to chordal graphs

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

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    Natural Language Statement

    Definition

    The minimum number of vertices whose deletion leaves a graph with no induced cycle of length at least four.

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    DefinitionThis conceptRelated conceptA → B: B builds on A

    Lean source view on GitHub

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