The geometric realization |C| of the complex consists of a copy of the unit interval [0,1] per edge, with the endpoints of these intervals glued together at vertices.
[2] John Hopcroft and Robert Tarjan[3] derived a means of testing the planarity of a graph in time linear to the number of edges.
Their algorithm does this by constructing a graph embedding which they term a "palm tree".
Efficient planarity testing is fundamental to graph drawing.
Fan Chung et al[4] studied the problem of embedding a graph into a book with the graph's vertices in a line along the spine of the book.