MO412 - Melissa Araújo

You’ve been waiting in the hospital waiting room for a long time. After staring at the artwork for so long, you begin to notice that the drawings in the frames look a lot like graphs. To pass the time, you decide to figure out which graphs are planar and which are not. The figure below illustrates how you see the artworks on the hospital wall. Select the option below that contains only frames whose drawings represent planar graphs: A) Frame 1, Frame 2, and Frame 3; B) Frame 1 and Frame 2; C) Only Frame 1; D) Only Frame 3; E) None of the above. Original idea by: Melissa Araújo.

Cynthya is a big fan of the band Suplaz, which rarely performs in Brazil. She just found out they’ll be at Rock in Rio and is thrilled. She is the manager of the Capanema (Pará) Suplaz fan group, so she decides to organize transportation to help as many fans from her city as possible attend the concert.  Since the trip is long, she sets up a system of shared rides and transfers: fans can travel between cities using different cars, vans, or buses, meeting at stops along the way. At each segment of the trip, there is a limit to how many people can be transported, depending on vehicle availability. Fans may switch vehicles at intermediate stops. The figure above represents this transportation system as a directed network. Capanema is the source (S) and Rock in Rio is the sink (T). The intermediate nodes (A, B, C, and D) represent transfer points, like hotels or meeting locations. Each edge has a capacity, indicating the maximum number of people that can travel along that segment. Usin...