It is known that any graph can be embedded into a three-dimensional space.<ref name="3d-gd"/>
One method for doing this is to place the points on any line in space and to draw the{{Clarify|reason=[[Talk:Graph_embedding#m_edges.3F|what 'm' edges? - discuss]]see talk page}} ''m'' edges as curves each of which lies in one of ''m'' distinct [[halfplane]]s having that line as their common boundary. An embedding like this in which the edges are drawn on halfplanes is called a [[book embedding]] of the graph. This [[metaphor]] comes from imagining that each of the planes where an edge is drawn is like a page of a book. It was observed that in fact several edges may be drawn in the same "page"; the ''book thickness'' of the graph is the minimum number of halfplanes needed for such a drawing.
Alternatively, any graph can be drawn with straight-line edges in three dimensions without crossings by placing its vertices in [[general position]] so that no four are coplanar. For instance, this may be achieved by placing the ''i''th vertex at the point (''i'',''i''<sup>2</sup>,''i''<sup>3</sup>) of the [[moment curve]].
