Discrete Mathematics with Graph Theory (3rd Edition) 394

Discrete Mathematics with Graph Theory (3rd Edition) 394 -...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
392 Solutions to Exercises (b) After the first night, we remove the edges corresponding to the dates which occurred. We are left with a bipartite graph in which every vertex has degree 4. Again, Problem 6 guarantees a perfect matching. Continue for the five nights, reducing the degree by 1 each time. 6. (a) [BB] Bruce +-t Maurice, Edgar +-t Michael, Eric +-t Roland, Herb +-t Richard. (b) If Roland and Bruce share a canoe, then Maurice and Michael would both have to be with Edgar. (c) No. If Bruce and Roland were together, then both Maurice and Michael would have to be in the same canoe with Edgar. On the other hand, if Bruce and Roland were not in the same canoe, then Bruce and Roland would have to be in the same canoe with Maurice and Michael (in some order), leaving no one for Edgar since he refuses to be with Herb. 7. (a) [BB] Construct a bipartite graph with vertex sets VI and V2, where VI has n vertices corresponding to AI, ... , An, V2 has one vertex for each element of S and there is an edge joining
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

Ask a homework question - tutors are online