Homework 3

# Homework 3 - CS180 Winter 2011 Homework 3 The following...

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CS180 Winter 2011 Homework 3 The following homework is due Wednesday, January 26 at the beginning of lecture. When submitting your homework, please include your name at the top of each page. If you submit multiple pages, please staple them together. We also ask that you do something to indicate which name is your last name on the ﬁrst page, such as underlining it. Please provide complete arguments and time complexity analysis for all solutions, unless otherwise stated. 1. Given a graph G , the Line Graph G 0 of G is a graph where all edges in G are vertices in G 0 . Two vertices in G 0 (which were edges in G ) have an edge between them iﬀ their edges in G are both incident to a common vertex. Prove or disprove: The line graph of a bipartite graph is a bipartite graph. 2. For an undirected connected graph G = ( V,E ), an Euler 1 Tour is an ordering t 1 ,t 2 ,...t m of edges such that any two consecutive edges in the ordering share a vertex and each edge appears once in the ordering. That is, it is a path that travels across each

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Homework 3 - CS180 Winter 2011 Homework 3 The following...

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