feat(ErdosProblems/1105): anti-Ramsey numbers for cycles and paths #1583
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Why did you close #1578? |
YaelDillies
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YaelDillies
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Jan 10, 2026
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| /-- An edge coloring of a simple graph `G` with color type `α`. | ||
| Note: this exists in upstream Mathlib as SimpleGraph.EdgeLabeling -/ | ||
| def EdgeColoring (G : SimpleGraph V) (α : Type*) := G.edgeSet → α |
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Can you keep the mathlib name?
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| /-- A graph `G` contains a rainbow copy of `H` if there is a subgraph of `G` that is isomorphic | ||
| to `H` and is rainbow under the edge coloring `c`. -/ | ||
| def HasRainbowCopy {V W : Type*} {G : SimpleGraph V} {α : Type*} (c : EdgeColoring G α) | ||
| (H : SimpleGraph W) : Prop := | ||
| ∃ (S : G.Subgraph), H ⊑ S.coe ∧ IsRainbow c S |
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Although your definition is equivalent, it is not the one your docstring describes (containment instead of iso). Can you make them match?
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| /-- A graph `G` contains a rainbow copy of `H` if there is a subgraph of `G` that is isomorphic | |
| to `H` and is rainbow under the edge coloring `c`. -/ | |
| def HasRainbowCopy {V W : Type*} {G : SimpleGraph V} {α : Type*} (c : EdgeColoring G α) | |
| (H : SimpleGraph W) : Prop := | |
| ∃ (S : G.Subgraph), H ⊑ S.coe ∧ IsRainbow c S | |
| /-- A graph `G` contains a rainbow copy of `H` if there is a subgraph of `G` that is isomorphic | |
| to `H` and is rainbow under the edge coloring `c`. -/ | |
| def HasRainbowCopy {V W : Type*} {G : SimpleGraph V} {α : Type*} (c : EdgeColoring G α) | |
| (H : SimpleGraph W) : Prop := | |
| ∃ (S : G.Subgraph), H \equivg S.coe ∧ IsRainbow c S |
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Can you move your new material to a new .EdgeLabeling file?
| open SimpleGraph | ||
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| def pathGraph (k : ℕ) : SimpleGraph (Fin k) := | ||
| SimpleGraph.fromRel fun i j => i.val + 1 = j.val |
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| SimpleGraph.fromRel fun i j => i.val + 1 = j.val | |
| hasse (Fin k) |
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This file introduces the Erdős Problem 1105, detailing conjectures related to anti-Ramsey numbers for cycles and paths. It includes definitions for edge coloring, rainbow subgraphs, and the anti-Ramsey number, along with theorems related to these conjectures.