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quiz02bs - The University of Sydney School of Mathematics...

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The University of Sydney School of Mathematics and Statistics Solutions to Quiz 2 MATH2069/2969: Discrete Mathematics and Graph Theory Semester 1, 2009 Name: SID: Enrolled in (please circle): MATH2069 MATH2969 This quiz lasts 30 minutes. There are a total of 30 marks. Note that the true/false parts of question 7 are worth half a mark each. Answers must be written in pen in the boxes provided. Anything written in pencil or written outside the boxes will not be marked.
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1. Complete the following definitions. (a) If v and w are vertices of a graph G , we say that v is linked to w in G if there is a walk from v to w in G . (b) If v is a vertex of a graph G , the degree deg( v ) is the number of edges ending at v . (c) A connected graph with 3 vertices is Hamiltonian if it has a walk which returns to its starting vertex and visits every vertex exactly once. (d) In a connected weighted graph, the Chinese Postman Problem is to find a walk which has minimal weight subject to the following constraints: it must
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