SimpleGraph.exists_maximal_degree_vertex

∀ {V : Type u_1} (G : SimpleGraph V) [inst : Fintype V] [inst_1 : DecidableRel G.Adj] [Nonempty V],
  ∃ v, G.maxDegree = G.degree v

There exists a vertex of maximal degree. Note the assumption of being nonempty is necessary, as the lemma implies there exists a vertex.

Defined in: Mathlib.Combinatorics.SimpleGraph.Finite
Cited by: 3 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype DecidableRel Nonempty

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