ass5 - MATH 239 Assignment 5 This assignment is due at noon...

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MATH 239 Assignment 5 This assignment is due at noon on Friday, July 10, 2009, in the drop boxes opposite the Tutorial Centre, MC 4067. Note: The notation e = uv is a shorthand for e = { u,v } . Even though we use the shorthand here, it is always understood that an edge is a subset of the vertices of size 2. 1. For each of the following descriptions of possible graphs, either show that one exists by drawing an example, or prove that such a graph does not exist. (a) A 3-regular graph that contains a bridge. (b) A 4-regular graph that contains a bridge. (c) A graph whose minimum degree is 4 (i.e. every vertex has degree at least 4) that contains a bridge. 2. Determine the minimum number of vertices r in any tree T having two vertices of degree 3, two vertices of degree 4, and one vertex of degree 6. Show that your answer is best possible by giving an example of such a tree with exactly r vertices. 3. Let

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ass5 - MATH 239 Assignment 5 This assignment is due at noon...

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