5.2.4. Minimum Separator Lemma

Try these first

1. 1.

   What is Kruskal's algorithm used for?

   Hint

   Think about what a spanning tree does.

2. 2.

   What does the Minimum Separator Lemma state?

   Hint

   Consider how edges connect different parts of a graph.

3. 3.

   What does Kruskal's algorithm primarily do?

   • Finds shortest paths
   • Finds minimum spanning trees
   • Counts edges

   Hint

   Think about the algorithm's purpose.

4. 4.

   True or False: The Minimum Separator Lemma states that any edge can be part of a minimum spanning tree.

   • True
   • False

   Hint

   Consider what the lemma specifically entails.

5. 5.

   Given a graph with vertices A, B, C, and D with edges AB (weight 2), AC (weight 1), and AD (weight 4), apply Kruskal's algorithm and explain your choices.

   Hint

   Focus on the smallest weights first.

6. 6.

   Design a graph example where the Minimum Separator Lemma does not apply and explain.

   Hint

   Think about the connectivity condition for the lemma.