Question: Graph Theory 1. Which trees are planar? Explain why? 2. Which complete graphs are planar? Explain why? 3. Suppose G' is a planar graph with

Graph Theory

1. Which trees are planar? Explain why? 2. Which complete graphs are planar? Explain why? 3. Suppose G' is a planar graph with four faces of lengths 3, 4, 5, 6. How many edges are there in G? 4. Suppose G is a planar graph having 67 edges. If each face of G' has length at least 6, then what is the maximum number of faces this graph can have? 5. Suppose G is an n-vertex planar graph in which each cycle has length at least 6. Find the best upper bound for the number of edges of G. (Hint: use a similar technique as we did in class, when we proved each planar graph has at most 3n-6 edges)

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