25.2.1. Summary of Key Concepts

Try these first

1. 1.

   Define a bipartite graph.

   Hint

   Think about the two distinct groups connected by edges.

2. 2.

   What is maximum matching?

   Hint

   Maximum means the highest count.

3. 3.

   What is a bipartite graph?

   • A graph with cycles
   • A graph that can be colored with two colors
   • A graph formed of disjoint vertex sets

   Hint

   Visualize the two groups in the graph.

4. 4.

   True or False: A complete matching occurs when all vertices match in a bipartite graph.

   • True
   • False

   Hint

   Think about what it means to match everyone.

5. 5.

   Given a bipartite graph of six employees and four modules, illustrate the maximum matching possible and demonstrate why finding a complete matching is difficult.

   Hint

   Focus on the interconnections between tasks and available resources.

6. 6.

   Design a scenario representing Hall's Marriage Theorem where certain employees cannot meet the job requirements and illustrate it using a bipartite graph.

   Hint

   Evaluate subsets carefully to determine neighbor counts.