1. MATCHINGS A college dramatic society has six helpers: Andrew, Donna, Henry, Karl, Nicola and Yana. They are to be matched to six tasks: Props, Lighting, Make-up, Sound, Tickets and Wardrobe. The table indicates which tasks each person is able to do. NameTasks AndrewWardrobe, Props, Tickets DonnaTickets, Make-up HenryLighting, Make-up KarlSound, Wardrobe, Lighting NicolaSound YanaLighting, Tickets

2. This is represented by the following Bipartite Graph: Initially, Andrew, Donna, Henry & Karl are matched to the first task in their list. As N is unmatched, we use N as the starting point of an alternating path. N  S = K  L = H  M N can do S S is being done by K K can do L L is being done by H H can do M BREAKTHROUGH Change status N = S — K = L — H = M Add NS, KL, HM Remove SK, LH We now have 5 people matched We apply the algorithm once more to improve the matching As Y is unmatched, we use Y as the starting point of an alternating path Y — L = K — W = A — P Change status Y = L — K = W — A = P Add YL, KW, AP Remove LK, WA All 6 people are now matched to 6 different jobs This is a maximal matching BREAKTHROUGH

3. Remember to state the final matching when you have finished Andrew – Props Donna – Tickets Henry – Make-up Karl – Wardrobe Nicola – Sound Yana - Lighting