Determine whether or not there is a known polynomial$-$time algorithm for solving the problem $($Hamilton Cycle, Travelling salesman problem, Vertex cover, Independent Set, Finding Cliques, Subset Sum, OR Dominating Set$).$

You must justify why there is no known poly$-$time algorithm OR identify a poly$-$time procedure that solves the problem.

Graph G is a simple, connected, undirected graph. There are n vertices and m edges The goal is to find at least k vertices that can be colored pink, and the remaining n$-$k vertices that can be colored blue, in such a way that no two pink vertices share an edge, and no two blue vertices share an edge. Note that each vertex must be colored either pink or blue.