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Unformatted text preview: Stratford . 3. Let G be graph with girth 5 and minimum degree ≥ d . (a) (2 points) For d = 3, draw such a graph with exactly d 2 + 1 vertices. (b) (3 points) Prove that any graph G with girth 5 and minimum degree ≥ d has at least d 2 + 1 vertices. 4. (3 points) Show that graph G as given in Figure 2 is planar by giving a planar embed-ding. 5. (3 points) Show that every planar bipartite graph has a vertex of degree at most 3. Math 239 Assignment 8 Due date: Friday, July 8 2011. d c b a o n m l k j i h g f e Figure 2: Graph G . 6. A planar triangulation is a connected planar embedding in which each face has degree 3. (a) (3 points) Show that every planar graph with at least 3 vertices is a spanning subgraph of a planar triangulation. (b) (3 points) Show that every planar triangulation with p vertices has 3 p-6 edges. Page 2...
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This note was uploaded on 08/13/2011 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.
- Spring '09