Abscissa and ordinate is the distance between the projection and the origin of the axis, and whose sign is given by the location on the projection relative to the origin (before: negative; after: positive). Usually these are the horizontal and vertical coordinates of a point in a two-dimensional rectangular Cartesian coordinate system. The terms can also refer to the horizontal and vertical axes respectively (typically "x"-axis and "y"–axis) of a two-dimensional graph. An ordered pair consists of two terms—the abscissa (horizontal, usually "x") and the ordinate (vertical, usually "y")—which define the location of a point in two-dimensional rectangular space. Though the word "abscissa"
Topological graph embeddings of graphs in surfaces (that is, drawings without crossings). A fundamental problem in extremal graph theory is the following: what is the maximum number of edges that a graph of "n" vertices can have if it contains no subgraph belonging to a given class of "forbidden subgraphs"? The prototype of such results is Turán's theorem, where there is one forbidden subgraph: a complete graph with "k" vertices ("k" is fixed). Analogous questions can be raised for topological and geometric graphs, with the difference that now certain "geometric subconfigurations" are forbidden. Historically, the first instance of such a theorem is