FormalConjecturesForMathlib.Combinatorics.SimpleGraph.LargestInducedTree

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module

public import Mathlib.Combinatorics.SimpleGraph.Acyclic
public import Mathlib.Combinatorics.SimpleGraph.Basic
public import Mathlib.Combinatorics.SimpleGraph.Finite

@[expose] public section

Largest induced tree

This file defines largestInducedTreeSize, the number of vertices in a largest induced subtree of a graph.

namespace SimpleGraphvariable {α : Type*} [Fintype α] [DecidableEq α]

largestInducedTreeSize G is the number of vertices in a largest induced subtree of G. A tree is a connected acyclic graph; an induced tree is an induced subgraph that is a tree.

noncomputable def largestInducedTreeSize (G : SimpleGraph α) : ℕ :=
  sSup { n | ∃ s : Finset α, s.card = n ∧ (G.induce (s : Set α)).IsTree }

end SimpleGraph