lidangzzz / R55-is-NOT-43

The 100-year-old math problem the Ramsey Number: R(5,5) ≠ 43.

Ramsey Number R(5,5) is NOT 43 (R55-is-NOT-43)

一些中文版本的补充

TL;DR

• Let's try to solve the 100-year-old math problem: The Ramsey Number: R(5,5) ≠ 43 together!
• Let's build The Easiest volunteer computing framework in 30 lines of code!
• Let's build The Real cross-platform volunteer computing client code which EXECUTING TOTALLY IN YOUR BROWSER without installation or configuration -- just open and run!
• Let's build a serverless Google Cloud Function as a server for volunteer computing framework in 30 lines of code!
• Let's solve the great math problem together!

0. How to join?

Here it is:

https://hedgehog-lab.github.io/?your_url=https://raw.githubusercontent.com/lidangzzz/R55-is-NOT-43/main/lets-find-ramsey-5-5-now.js&auto_run=true

1. What is Ramsey Number?

Ramsey number is math problem that finding the minimum number of vertices k = R(m,n) so that any undirected graph with k vertices always contains a clique of m or an independent set of m.

Current roadmap of Ramsey Numbers on Wolfram: https://mathworld.wolfram.com/RamseyNumber.html

2. What is latest updates on R(5,5)?

R(5,5) is the next Ramsey number with m=n that is not totally solved yet. Here are the latest updates:

• In 1989, Geoffrey Exoo found the lower bound of R(5,5)>=43 at 1989.
• In 2019, Vigleik Angeltveit and Brendan D. Mckay found the upper bound of R(5,5)<=48 at https://arxiv.org/pdf/1703.08768.pdf.
• The latest update about upper bound of Ramsy number is from Ashwin Sah at https://arxiv.org/pdf/2005.09251.pdf.

3. What's the idea of this project?

The time complexity is extremely huge to go through every single nonisomorphic graph with 43 vertices. Brendan McKay mentioned that it takes 10^60 years with a brute-force method. So we want to try another volunteer-computing approach. For each volunteer:

1. Generate a random graph G with 43 vertices randomly;
2. Find the maximum clique number m;
3. Find the maximum independent set n;
4. If m<5 and n<5, return the graph G.

Still the probablity of finding valid graph that prove R(5,5) ≠ 43 is extremely small, but from the perspective of volunteer-computing, it's much easier than the traversal of all graph networks.

4. Where is the source code? Is it harmful?

The source code is here: https://github.com/lidangzzz/R55-is-NOT-43/blob/main/lets-find-ramsey-5-5-now.js. No malicious or bitcoin mining scripts are included.