Finishing when all the vertices of g have been

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finishing when all the vertices of G have been reached. (Ties are broken arbitrarily.) Prove that Prim’s Algorithm produces a minimum weight spanning tree. 5 . Let C be a cycle in a connected weighted graph in G . Let e be an edge of maximum weight on C . Prove that there is a minimum spanning tree not containing e . Use this to prove that iteratively deleting a heaviest non cut-edge until no such edge exists produces a minimum weight spanning tree. 6 . Two people play a game on a graph G , alternately choosing distinct vertices. The first player starts by choosing any vertex. Each subsequent choice must be adjacent to the preceding choice (of the other player). Thus together they follow a path. The last player able to move wins. Prove that the second player has a winning strategy if G has a perfect matching and the first player has a winning strategy if G does not have a perfect matching. —————————————————— Problems below review basic concepts and their ideas could be used in the tests. WARMUP PROBLEMS: Section 2.3: # 2, 3. Section 3.1: # 1, 2, 3, 4, 6. Do not write these up! OTHER INTERESTING PROBLEMS: Section 2.2: # 23 Section 3.1: # 8, 9, 10, 21, 24, 25, 30. Do not write these up! 1
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  • Spring '13
  • Dr.ZAre
  • Graph Theory, credit hour course, minimum weight, connected weighted graph, minimum weight spanning, weighted complete graph

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