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Combinatorics / CONCEPT

Upsets in neighbourhood convex geometries

Let V be any finite nonempty vertex set and G any simple undirected graph on V. Closed neighbourhoods include their centre. No connectivity, absence of universal vertices, or distinction of equal neighbourhoods is assumed.

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THEOREM

Every upset is neighbourhood-convex

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Upsets in neighbourhood convex geometriesUpsets in neighbourhood convexgeometries
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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/Graph/BubboloniCaceresNeighbourhoodUpsets
Repository path
D5/S3/Combinatorics/Graph/BubboloniCaceresNeighbourhoodUpsets.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
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37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.