Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.pathGraph

(n : ℕ) → SimpleGraph (Fin n)

The path graph on n vertices.

Defined in
Mathlib.Combinatorics.SimpleGraph.Hasse
Cited by
8 results in Mathlib
Foundations
Depth 25 from the axioms · uses propext, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

SimpleGraph.pathGraph_le_cycleGraph · cited by 2SimpleGraph.pathGraph_le_…SimpleGraph.pathGraph_preconnected · cited by 2SimpleGraph.pathGraph_pre…SimpleGraph.pathGraph3ComplEmbeddingOf · cited by 1SimpleGraph.pathGraph3Com…SimpleGraph.pathGraph_adj · cited by 1SimpleGraph.pathGraph_adjSimpleGraph.pathGraph_connected · cited by 1SimpleGraph.pathGraph_con…SimpleGraph.Walk.IsPath.pathGraphCopy · cited by 1IsPath.pathGraphCopySimpleGraph.not_isCompleteMultipartite_of_pathGraph3ComplEmbedding · cited by 1SimpleGraph.not_isComplet…SimpleGraph.pathGraph.bicoloring · cited by 1pathGraph.bicoloringSimpleGraph.pathGraph_two_embedding · cited by 0SimpleGraph.pathGraph_two…SimpleGraph.pathGraph_two_eq_top · cited by 0SimpleGraph.pathGraph_two…SimpleGraph.Walk.IsPath.isContained_pathGraph · cited by 0IsPath.isContained_pathGr…SimpleGraph.IsPathGraph3Compl.pathGraph3ComplEmbedding · cited by 0IsPathGraph3Compl.pathGra…SimpleGraph.Walk.IsPath.pathGraphIsoToSubgraph · cited by 0IsPath.pathGraphIsoToSubg…SimpleGraph.chromaticNumber_pathGraph · cited by 0SimpleGraph.chromaticNumb…SimpleGraph.Walk.pathGraphHom · cited by 0Walk.pathGraphHomSimpleGraph · cited by 3072SimpleGraphSimpleGraph.hasse · cited by 8SimpleGraph.hasseSimpleGraph.pathGraphCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by16

Results whose statement or proof uses this declaration.