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Sandwich conjecture

A conjecture in random graph theory, due to Jeong Han Kim and Van Ha Vu, holding that a random regular graph with a reasonable number of edges can almost always be placed between two random binomial graphs, one contained in it and one containing it.

Known aliases

graph sandwich conjecture
Kim-Vu sandwich conjecture

Relationships

No evidence-backed relationships are recorded.

Current clusters

science1 publisher

Random regular graphs can now inherit their properties from the easier random model

The sandwich conjecture that Jeong Han Kim and Van Ha Vu posed in 2004 was proved in 2025, so a property established for a random binomial graph now carries to the regular graph containing it, once the graph is large enough.

Publishers:quantamagazine.org

Reality

Evidence58
Adoption: Insufficient
Hype gap+12
Incentives32
Confidence54