T8 - 3 Deduce from this that every triangle-free planar...

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MATH 239: Problems for Tutorial 8 July 12, 2010 1. Let P be the Petersen graph. (a) Show that if any edge of P is deleted, the resulting graph is non- planar. (b) Show that there exists a set of two edges which, when deleted, result in a planar graph. (c) Show that there exists a set of two edges which, when deleted, result in a non-planar graph. 2. Prove that every triangle-free planar graph has a vertex of degree at most
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Unformatted text preview: 3. Deduce from this that every triangle-free planar graph is 4-colourable. 3. Give a complete list of the connected, planar, self-dual, regular graphs which have at least one edge. 4. Let G be a connected 4-regular planar graph on 10 vertices. What we can say about the face degrees of an embedding of such a graph? Give an example of such a graph. 1...
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This note was uploaded on 11/26/2011 for the course MATH 239 taught by Professor M.pei during the Spring '09 term at Waterloo.

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