Generating simple drawings of graphs

In this thesis, we study the crossing numbers of complete graphs. After introducing a long history of the old problem of determining the crossing number of Kn, we survey the recent progress on the Harary-Hill conjecture by compiling proofs of this conjecture for special classes of drawings of Kn. We also create a program for generating a database of all simple drawings of Kn with n ≤ 8. We implement another program that visualizes these drawings and allows the user to create its own simple drawings of general graphs. The visualizer also captures the structure of crossings of the displayed drawings. We use our programs to verify a conjecture by Balko, Fulek, and Kynčl for small cases and we find a mistake in a paper by Mutzel and Oettershagen.