Hypergraphs Reveal a Solution to a 50-Year-Old Problem

The goal here is to trace out triangles on top of these lines such that the triangles satisfy two requirements: First, no two triangles share an edge. (Systems that fulfill this requirement are called Steiner triple systems.) And second, ensure that every small subset of triangles utilizes a sufficiently large number of nodes.

The way the researchers did this is perhaps best understood with an analogy.

Say that instead of making triangles out of edges, you’re building houses out of Lego bricks. The first few buildings you make are extravagant, with structural reinforcements and elaborate ornamentation. Once you’re done with these, set them aside. They’ll serve as an “absorber”—a kind of

→ Continue reading at Wired - Science

More from author

Related posts

Advertisment

Latest posts

The Tantalizing Mystery of the Solar System’s Hidden Oceans

The original version of this story appeared in Quanta Magazine.For most of humankind’s existence, Earth was the only known ocean-draped world, seemingly unlike any...

The Role of Scholarships and Grants in Financing Education

Applying for scholarships and grants helps students pay for college. In some situations, these awards allow people to obtain a degree they wouldn't be...

EV, hybrid and gas-powered: Some interesting cars coming in 2024 | CNN Business

CNN  —  Next year will see the introduction of some new, genuinely affordable electric vehicles as well as...