feat(Combinatorics/SimpleGraph/StarGraph): define star graphs#38027
feat(Combinatorics/SimpleGraph/StarGraph): define star graphs#380278e7 wants to merge 12 commits intoleanprover-community:masterfrom
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PR summary 2ff88851d5Import changes for modified filesNo significant changes to the import graph Import changes for all files
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Please mark the review comments 'resolved' once you've addressed them so the next reviewer doesn't think they're still open. |
Co-authored-by: Vlad Tsyrklevich <vlad902@gmail.com>
IvanRenison
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I like the idea!
Maybe we should have StarGraph in a separate graph
| · refine isAcyclic_iff_forall_adj_isBridge.mpr fun _ _ hadj ↦ ?_ | ||
| exact isBridge_iff_adj_and_not_isEdgeConnected_two.mpr ⟨hadj, h hadj.ne⟩ | ||
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| section Star |
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How about moving this to a new file that imports Acyclic.lean?
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I suggested the same. I think it is a good idea to have it in a new file
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I agree to putting it in a new file. I'm considering adding some lemmas to characterize the metric of a star graph, as well as defining isomorphism between star graphs. Should I add these lemmas, or should I leave them for a future PR?
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I would add them in a separate pull request, to keep each pull request small, but both ways of doing it are okay
Co-authored-by: Snir Broshi <26556598+SnirBroshi@users.noreply.github.com>
Co-authored-by: Iván Renison <85908989+IvanRenison@users.noreply.github.com>
8e7
changed the title
| lemma isTree_starGraph (r : V) : (starGraph r).IsTree := by | ||
| refine ⟨connected_starGraph r, isAcyclic_starGraph r⟩ |
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| lemma isTree_starGraph (r : V) : (starGraph r).IsTree := by | |
| refine ⟨connected_starGraph r, isAcyclic_starGraph r⟩ | |
| lemma isTree_starGraph (r : V) : (starGraph r).IsTree := | |
| ⟨connected_starGraph r, isAcyclic_starGraph r⟩ |
| rw [degree, neighborFinset_eq_filter (starGraph r)] | ||
| simp only [starGraph_adj, ne_eq, true_or, and_true] | ||
| have : ({w | ¬r = w} : Finset V) = Finset.univ.erase r := by | ||
| ext v; simp [eq_comm] | ||
| rw [this, Finset.card_erase_of_mem (Finset.mem_univ r), Finset.card_univ] |
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| rw [degree, neighborFinset_eq_filter (starGraph r)] | |
| simp only [starGraph_adj, ne_eq, true_or, and_true] | |
| have : ({w | ¬r = w} : Finset V) = Finset.univ.erase r := by | |
| ext v; simp [eq_comm] | |
| rw [this, Finset.card_erase_of_mem (Finset.mem_univ r), Finset.card_univ] | |
| simp [degree, neighborFinset_eq_filter (starGraph r), starGraph_adj, Finset.univ.filter_ne r] |
| · have hw : w = r := hadj.2.resolve_left h | ||
| replace hadj : w ≠ v ∧ (w = r ∨ v = r) := ⟨hadj.1.symm, hadj.2.symm⟩ | ||
| rw [reachable_comm, Sym2.eq_swap] | ||
| exact this r w v hadj hw |
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| · have hw : w = r := hadj.2.resolve_left h | |
| replace hadj : w ≠ v ∧ (w = r ∨ v = r) := ⟨hadj.1.symm, hadj.2.symm⟩ | |
| rw [reachable_comm, Sym2.eq_swap] | |
| exact this r w v hadj hw | |
| · rw [reachable_comm, Sym2.eq_swap] | |
| exact this r w v ⟨hadj.1.symm, hadj.2.symm⟩ (hadj.2.resolve_left h) |
| exact this r w v hadj hw | ||
| · subst h | ||
| apply not_reachable_of_neighborSet_right_eq_empty hadj.1 | ||
| ext x; aesop |
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| ext x; aesop | |
| ext x | |
| aesop |
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Add a new definition
starGraphand several key lemmas. Star graphs are a trivial class of tree, often used in constructive proofs regarding trees.All lemmas are hand written first, then golfed with the help of Claude Code.