Theorems · Theorem · combinatorics
SimpleGraph.Colorable.chromaticNumber_le
∀ {V : Type u} {G : SimpleGraph V} {n : ℕ}, G.Colorable n → G.chromaticNumber ≤ ↑n- Cited by
- 11 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement and proof · cited by 4,985
- SimpleGraphstatement and proof · cited by 3,072
- SimpleGraph.Colorablestatement and proof · cited by 67
- SimpleGraph.chromaticNumberstatement · cited by 54
- csInf_leproof · cited by 51
- SimpleGraph.Colorable.chromaticNumber_eq_sInfproof · cited by 5
- SimpleGraph.chromaticNumber_bddBelowproof · cited by 1
Cited by11
Results whose statement or proof uses this declaration.
- SimpleGraph.chromaticNumber_le_iff_colorableproof · cited by 10
- SimpleGraph.chromaticNumber_eq_card_iff_forall_surjectiveproof · cited by 1
- SimpleGraph.chromaticNumber_eq_iff_forall_surjectiveproof · cited by 1
- SimpleGraph.chromaticNumber_pathGraphproof · cited by 0
- SimpleGraph.IsTree.chromaticNumber_le_twoproof · cited by 0
- SimpleGraph.IsAcyclic.chromaticNumber_le_twoproof · cited by 0
- SimpleGraph.chromaticNumber_botproof · cited by 0
- SimpleGraph.chromaticNumber_cycleGraph_of_evenproof · cited by 0
- SimpleGraph.chromaticNumber_cycleGraph_of_oddproof · cited by 0
- SimpleGraph.two_colorable_iff_forall_loop_evenproof · cited by 0
- SimpleGraph.completeMultipartiteGraph.chromaticNumberproof · cited by 0