1 Prove Hall s Marriage Theorem and provide an original example where Hall s condition holds and and an original does not hold

Question

1 Prove Hall s Marriage Theorem and provide an original example where Hall s condition holds and and an original does not hold respectively 2 For the following graph find all shortest paths from Node 1 to Node 5 using labelling method with depth first breadth first and Dijkstra schemes Explain how dynamic programming can be used for this task Explain in general the advantages and this advantages of these four methods 1 2 counterexample 1 2 3 1 3 0 4 0 5

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