Kuratowski's theorem Quiz

1. Which two graphs appear in Kuratowski's theorem?

• A. $K_4$ and $K_{2,3}$
• B. $K_5$ and $K_{3,3}$
• C. $K_5$ and $K_{2,2}$
• D. $K_6$ and $K_{4,4}$

2. A subdivision of $K_{3,3}$ is made by adding one vertex of degree 2 to an edge. How many edges does it have?

• A. $9$
• B. $11$
• C. $12$
• D. $10$

3. A graph has 8 edges. Which statement is true?

• A. It must be planar
• B. It must be non-planar
• C. It could be either
• D. It must contain $K_5$

4. Which of these is planar?

• A. $K_5$
• B. $K_{3,3}$
• C. $K_4$
• D. A subdivision of $K_5$

5. One edge is deleted from $K_{3,3}$. What can be said?

• A. It is non-planar because it still contains $K_5$
• B. It is non-planar because every vertex has degree at least 2
• C. It cannot be decided
• D. It is planar: it has only 8 edges, too few for a subdivision of either graph