Question 6 and 7 need to be done

Consider taking El = aN, i.e., the total number of edges is proportional to the number of vertices. This is a relatively sparse number of edges, given the total number of edges that can exist between A and B. 6) Show that taking El = 3N, the expected number of matchings goes to 0 as N +0. (5 points) 2 7) Show that taking |E| = 4N, the expected number of matchings goes to infinity as N +0. (5 points) Consider taking El = aN, i.e., the total number of edges is proportional to the number of vertices. This is a relatively sparse number of edges, given the total number of edges that can exist between A and B. 6) Show that taking El = 3N, the expected number of matchings goes to 0 as N +0. (5 points) 2 7) Show that taking |E| = 4N, the expected number of matchings goes to infinity as N +0. (5 points)