Finding the maximal independent sets with dynamical systems

Finding maximal independent sets is a classical problem in
graph theory. We extend the related concepts in graph theory to
k-uniform hypergraphs (k-graphs), attempting to find the maximal
independent sets in k-graphs using a dynamical systems approach. We
establish a new method for transforming the maximal independent set
problem into differential equations using the competitive
Lotka-Volterra equations, commonly used in Biomath, and we show that
the trajectories of these systems can converge to a state that
represents the indicator of a maximal independent set. In addition, we
discuss the application of this method in combinatorics and establish
a connection between this approach and the Lagrangian method for
finding maximal cliques in k-graphs.