# Harrison Chapman

## Math 301: Homework 9

Due: Friday, November 15, 2019

2. Is it possible to find a set of 20 edges from $$K_{10}$$, the complete graph on 10 vertices, such that if you remove those 20 edges then you obtain a planar graph? If so, draw such a graph as a planar map (with no edges crossing). If not, explain why not.
3. Prove that the graph $$K_{3,3}$$ is not planar without using Kuratowski’s theorem. Hint. Notice that there are no triangles (cycles of length 3) in the graph.