Model the following problem as a graph colouring problem: An airline is trying to decide if the 6 gates it has available at a major airport will be sufficient to accomodate its 30 planes. Each plane has a known time (between its arrival at the airport and departure from the airport) in which the plane must be at a gate, and a gate can have at most one plane at a time. Make sure to clearly state what exactly does the set of vertices V and edges E correspond to, and what is being coloured, the vertices or the edges?