syllabus

1. How many edges does a complete graph with 11 vertices have?

2. Draw a tournament with five vertices which has five cyclic triples. What is the score sequence of this tournament?

Think about, but don't hand in: Can the directions of some of the edges of the tournament in the previous problem be changed so as to give a tournament with more than five cyclic triples? Can the directions be changed to produce a tournament with exactly four cyclic triples?

3. For each of these three sequences

(a) (1, 1, 2, 2) (b) (0, 2, 2, 2) (c) (1, 1, 2, 3)

either draw a tournament having the sequence as a score
sequence, or explain why there is no such tournament,