Mathlib Map

Theorems · Definition · combinatorics

SimpleGraph.comap

{V : Type u_1} → {W : Type u_2} → (V → W) → SimpleGraph W → SimpleGraph V

Given a function, there is a contravariant induced map on graphs by pulling back the adjacency relation. This is one of the ways of creating induced graphs. See SimpleGraph.induce for a wrapper. This is surjective when f is injective (see SimpleGraph.comap_surjective).

Defined in
Mathlib.Combinatorics.SimpleGraph.Maps
Cited by
29 results in Mathlib
Foundations
Depth 10 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.induce · cited by 80SimpleGraph.induceSimpleGraph.completeEquipartiteGraph · cited by 12SimpleGraph.completeEquip…SimpleGraph.completeMultipartiteGraph · cited by 11SimpleGraph.completeMulti…Equiv.simpleGraph · cited by 4Equiv.simpleGraphSimpleGraph.Hom.le_comap · cited by 3Hom.le_comapSimpleGraph.comap_adj · cited by 3SimpleGraph.comap_adjSimpleGraph.comap_map_eq · cited by 3SimpleGraph.comap_map_eqSimpleGraph.map_le_iff_le_comap · cited by 3SimpleGraph.map_le_iff_le…SimpleGraph.Iso.comap · cited by 2Iso.comapSimpleGraph.comap_symm · cited by 2SimpleGraph.comap_symmSimpleGraph.comap_top · cited by 2SimpleGraph.comap_topSimpleGraph.Embedding.comap · cited by 2Embedding.comapSimpleGraph.Embedding.comap_eq · cited by 2Embedding.comap_eqSimpleGraph.le_comap_of_subsingleton · cited by 2SimpleGraph.le_comap_of_s…SimpleGraph.leftInverse_comap_map · cited by 2SimpleGraph.leftInverse_c…SimpleGraph · cited by 3072SimpleGraphSimpleGraph.Adj · cited by 1346SimpleGraph.AdjSimpleGraph.comapCITED BYCITES

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Cited by37

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