Topics on line segments and polygons (Q1916383)

For finite sets of pairwise disjoint line segments in the plane, figures such as simple polygons, simple paths, or trees are considered, where the condition is that the figure may only use the endpoints of the line segments and may not intersect any line segment properly. An example is given that shows that a simple polygonal chain that uses all line segments as edges, but has no additional vertices than the endpoints, doesn't always exist. Other versions of this type of problem allow the line segments to be diagonals of a polygon, or require that the figure use exactly one endpoint of each line segment.