Science
Mathematicians resolve long-standing graph sandwich conjecture
Researchers have completed a full proof for the 2004 conjecture, according to Hacker News.
The short version
- Mathematicians Richard Montgomery, Natalie Behague, and Daniel Iľkovič completed a full proof for the 2004 'sandwich conjecture' in 2025.[Hacker News]
- The breakthrough allows researchers to analyze complex random regular graphs by sandwiching them between simpler random binomial graphs.[Hacker News]
- The team developed a step-by-step process to build both types of graphs in tandem, resolving a problem that had previously only been partially proven.[Hacker News]
Key facts
- Jeong Han Kim and Van Ha Vu first hypothesized the graph sandwich conjecture in 2004.[Hacker News]
- Richard Montgomery, Natalie Behague, and Daniel Iľkovič completed the full proof of the conjecture in 2025.[Hacker News]
- The trio's construction method was heavily adapted from a 2019 result by mathematician Pu Gao and two colleagues.[Hacker News]
Sources
Outlet counts describe coverage, not independent confirmation. Reports may share a wire service or original source.