The Independent Set Algorithm

The Independent Set Algorithm, Volume 1, is a specialized research text in the field of mathematics. This work introduces a new polynomial-time algorithm designed to find maximal independent sets within graphs. The author utilizes this method to establish new bounds on Ramsey numbers based on the maximum and minimum vertex degrees of Ramsey graphs.

The text examines the P versus NP question by testing the algorithm against various complex graphs, including large benchmark examples with hidden maximum independent sets. This mathematics volume includes a C++ implementation of the algorithm and a demonstration program for Microsoft Windows. By focusing on the efficiency of finding maximum independent sets, the book provides a technical analysis of graph theory and computational complexity.