We prove that the maximum rectilinear crossing number of the Petersen graph is 49. First, we illustrate a picture of the Petersen graph with 49 crossings to prove the lower bound. We then prove that this bound is sharp by carefully analyzing the ten Cs's which occur in the Petersen graph and their properties.
Feder, Elie; Harborth, Heiko; Herzberg, Steven; and Klein, Sheldon, "The Maximum Rectilinear Crossing Number of the Petersen Graph" (2010). CUNY Academic Works.