EmbeddingGemma 2: an open, lightweight multimodal embedding model
deepmind.google·6d ago
AI Engineering
Hacker News·24d ago·5 min read
Mathematicians Build Long-Awaited Graph Sandwich
TL;DR
Three mathematicians have successfully proven the long-standing 'sandwich conjecture' in graph theory, demonstrating that complex graphs can be rigorously analyzed by placing them between simpler graphs.
✦ Why It Matters
Explore graph theory applications in your projects to leverage this new understanding.
Key Takeaways
- Utilize the sandwich conjecture to simplify graph property analysis.
- Explore new results emerging from the proof of the conjecture.
- Apply methods from the proof to study complex network structures.
- Investigate further connections between different types of random graphs.
How It Works
The mathematicians constructed a random regular graph and a random binomial graph simultaneously, ensuring that the regular graph always contained the binomial graph. They used a weighted coin-flipping method to add edges, adjusting the probabilities dynamically to maintain the properties of both graph types.