Mathematicians Build Long-Awaited Graph Sandwich
3 hours ago
- In 2004, mathematicians proposed a 'graph sandwich' to relate random binomial graphs and random regular graphs, transferring properties between them.
- The sandwich conjecture required building a regular graph that contains a binomial graph (bottom slice) and is contained in another binomial graph (top slice).
- After decades of partial progress, in 2025 three mathematicians (Behague, Iškovič, Montgomery) proved the conjecture using a step-by-step edge addition and removal method.
- The proof allows deriving many properties of random regular graphs from the well-studied binomial graphs automatically, serving as a meta-theorem.
- The result deepens the understanding of connections between constrained and unconstrained random processes and opens avenues for more complex graph sandwiches.