Pries Fall 2012: Introduction to Combinatorial Theory:
Sample questions for quiz 1.
Here are some sample questions. Make sure to look at the homework and handouts too since
not all topics are covered here.
1. How many edges are there in a complete graph with 7 vertices?
2. If G is a graph with 50 edges, what is the smallest number of vertices it can have?
3. Explain why the cube graph has no Euler cycle. What is the smallest number of edges
that you would need to add in order for it to have an Euler cycle?
4. For which number n does the complete bipartite graph K4,n have a Hamilton circuit?
Why?
5. Three couples are invited to dinner by one host. As they arrive, some of the guests
shake hands with each other and with the host. No person shakes hands with their
partner. Each of the guests shakes a different number of hands (possibly zero). The
guest Allison shakes the most hands.
a. How many hands did Allison shake?
b. How many hands did Allison’s partner shake?
c. How many hands did the host shake?
6. LPV: page 140 #7.3.5.
7. HHM: pg 9 # 5, pg 17 #8.