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\head{1390}{Algorithms}{Winter 2000}{17 February 2000}{13}

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  \Large{\bf Problem Set 4 (due February 24)}
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{\bf 1. (7 $\times$ 5 = 35 points)} Problem~23--1, page 495.  Assume
that the given graph does not have any self-loops.

{\bf 2. (10 points)} Exercise~23.3-8, page 485.  (The directed graph
should have no self-loops.)
  
{\bf 3. (20 points)} Exercise~23.4-5, page 488.

{\bf 4. (15 points)} Let $T$ be any minimum spanning tree of $G$.  Let
$T'$ be a spanning tree of $G$, not necessarily a minimum spanning
tree.  Prove or disprove the following statement: The largest edge
weight of $T$ is at most the largest edge weight of $T'$.

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