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sorrachai
reviewed
May 11, 2026
| Set.MapsTo f (components (deleteEdge G e)) | ||
| ((components G).disjSum {()}) ∧ | ||
| Set.InjOn f (components (deleteEdge G e)) := by | ||
| classical |
sorrachai
reviewed
May 11, 2026
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| /-- The subgraph induced by a finite vertex set. -/ | ||
| @[simp, grind] noncomputable def inducedSubgraph (G : SimpleGraph α) (C : Finset α) : | ||
| SimpleGraph α := by classical |
sorrachai
reviewed
May 11, 2026
| /-! ## Induced subgraphs and component-wise counting identities -/ | ||
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| /-- The subgraph induced by a finite vertex set. -/ | ||
| @[simp, grind] noncomputable def inducedSubgraph (G : SimpleGraph α) (C : Finset α) : |
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Can we avoid noncomputability? I want it to be computable by default.
sorrachai
reviewed
May 11, 2026
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| /- `componentOf G v` is the connected component containing `v`. -/ | ||
| /-- The connected component containing `v`. -/ | ||
| @[simp, grind] noncomputable def componentOf (G : SimpleGraph α) (v : Vertex G) : Finset α := by |
sorrachai
reviewed
May 11, 2026
| Reachable G u v → Reachable H u v) | ||
| (hNum : numComponents G = numComponents H): | ||
| ∀ u v : α, | ||
| u ∈ G.vertexSet → v ∈ G.vertexSet → Reachable H u v → Reachable G u v := by classical |
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Suggested change
| u ∈ G.vertexSet → v ∈ G.vertexSet → Reachable H u v → Reachable G u v := by classical | |
| ∀ u ∈ V(G), ∀ v ∈ V(G), H.Reachable u v → G.Reachable u v := by classical |
Try to use notation more. My general comment is that try to make sure that the statement looks like English.
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Add core graph-walk infrastructure and tree-related results for undirected simple graphs.
Split core walk definitions into
VertexSeqandWalkAdd helper lemmas for walk edge sets, vertex sequences, and walks in graphs
Add
deleteEdgefor simple graphsAdd component helper lemmas
Add bridge definitions and bridge-related lemmas
Add tree/forest definitions and tree's equivalence theorems