Special case of coloring a weighted graph

Question

The problem is: I have a graph G , where each vertex is labelled by some non-negative number (a weight), and I have to find the subset S of non-adjacent vertices (an independent set of G ) that maximizes the sum of their labels (let's call it W(S) , the weight of the subset S ).

It comes to my mind the world of graph coloring, but in this case, the problem is coloring the graph using only two colors, white for choosen verteces, and black otherwise, so that only white verteces must be non-adjacent while their total weight is maximized (or minimized if we make all labels negative).

Has this specific problem a name? The closest thing I have found is cocoloring , but they don't apply to weighted graphs.

Answer 1

Have a look at independent sets ( https://en.wikipedia.org/wiki/Independent_set_(graph_theory) ). Your particular problem is the maximum weight independent set problem.