No, the K5 graph (five "dots" connected each connected to the other four) is not planar: it cannot be drawn in the plane with no edge (i.e., connection line) crossings. The best you can do is one crossing, and the animation shows one way to acheive this. It is the smallest graph in terms of the number of vertices("dots") with this property. The graph K(3,3), the bipartite graph with 6 vertices, where three of the vertices are connected to the other three (but not to each other), has the fewest number of edges (9 compared to 10 for K5). It can also be drawn with one edge crossing, maybe I'll make an animation of that some time. cheers, Matt
