Mathematicians Finally Build the Long-Awaited Graph Sandwich

Mathematicians Build Long-Awaited Graph Sandwich

In 2004, Kim and Vu conjectured that any large enough random regular graph can be sandwiched between two random binomial graphs, letting hard properties transfer for free. Mathematicians had proved only pieces of it for two decades. Then in 2025, Richard Montgomery, Natalie Behague, and Daniel Iľkovič built the sandwich edge by edge, completing the proof and giving researchers a new tool for understanding complex networks.