Can you untangle the graph? Drag the vertices so that no two lines cross. Every graph here is solvable, as they’re all planar graphs. By Jason Davies.
Can you untangle the graph on a cylinder? Its left and right sides are joined, so whatever leaves one comes back on the other; its top and bottom are edges. Drag the vertices so that no two lines cross. Every graph here is solvable, as each was drawn on a cylinder first. Any graph that fits on a cylinder fits on a plane, too: it’s the wrapping that makes these harder. By Jason Davies.
Can you untangle the graph on a Möbius strip? Its left and right sides are joined with a twist, so whatever leaves one comes back on the other upside down; its top and bottom are its one edge. Drag the vertices so that no two lines cross. Every graph here is solvable, as each was drawn on a Möbius strip first. By Jason Davies.
Can you untangle the graph on a torus? Its opposite sides are joined, so whatever leaves one side comes back on the other. Drag the vertices so that no two lines cross. Every graph here is solvable, as they’re all toroidal graphs. By Jason Davies.
Can you untangle the graph on a Klein bottle? Its top and bottom are joined, and its left and right sides are joined with a twist, so whatever leaves one comes back on the other upside down. It has no edges, and no inside or outside. Drag the vertices so that no two lines cross. Every graph here is solvable, as each was drawn on a Klein bottle first. By Jason Davies.