Theorems · Theorem · combinatorics
SimpleGraph.minDegree_le_degree
∀ {V : Type u_1} (G : SimpleGraph V) [inst : Fintype V] [inst_1 : DecidableRel G.Adj] (v : V), G.minDegree ≤ G.degree vThe minimum degree in the graph is at most the degree of any particular vertex.
- Defined in
- Mathlib.Combinatorics.SimpleGraph.Finite
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableRel
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Fintypestatement and proof · cited by 7,736
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Adjstatement and proof · cited by 1,346
- Finset.mem_univproof · cited by 361
- SimpleGraph.neighborSetstatement · cited by 257
- SimpleGraph.degreestatement and proof · cited by 112
- Finset.mem_image_of_memproof · cited by 81
- SimpleGraph.minDegreestatement · cited by 25
- Finset.min_leproof · cited by 6
- WithTop.untopD_leproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- SimpleGraph.Copy.minDegree_monoproof · cited by 2
- SimpleGraph.minDegree_le_maxDegreeproof · cited by 1
- SimpleGraph.minDegree_le_minDegreeproof · cited by 1
- SimpleGraph.IsTree.minDegree_eq_one_of_nontrivialproof · cited by 0
- SimpleGraph.le_minDegree_induce_of_support_subsetproof · cited by 0