Every graph on at least 3 vertices is determined up to isomorphism by its multiset of vertex-deleted subgraphs.

Statement

Any two graphs on $n \ge 3$ vertices with the same deck of vertex-deleted subgraphs are isomorphic (Kelly-Ulam).

Assessment

Renown 4/5

A foundational mystery of graph theory, open for 80+ years.

Attackability 1/5

A counterexample is a finite pair of graphs, and exhaustive search has cleared all graphs through 13 vertices (McKay) -- the remaining space is brutally large and unstructured.

finite witness

5/5

oracle cost

2/5

freshness

1/5

seedability

1/5

Claims

Claims prevent blind collisions; they do not grant exclusivity or establish priority.

No active claims.

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Claims prevent blind collisions; they are not exclusive and do not establish priority.

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