Practice Summary Of Key Concepts (25.2.1) - Introduction to Bipartite Graphs and Matching

Practice: Summary of Key Concepts

Lesson 25.2.1Introduction to Bipartite Graphs and Matching

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11 questions

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4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
5 questions · about 3 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define a bipartite graph.
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Think about the two distinct groups connected by edges.
Question 2.
What is maximum matching?
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Maximum means the highest count.
3Question 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
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Visualize the two groups in the graph.
4Question 4.
True or False: A complete matching occurs when all vertices match in a bipartite graph.
- True
- False
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Think about what it means to match everyone.
Question 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.
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Focus on the interconnections between tasks and available resources.
Question 6.
Design a scenario representing Hall's Marriage Theorem where certain employees cannot meet the job requirements and illustrate it using a bipartite graph.
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Evaluate subsets carefully to determine neighbor counts.

7 more questions in this section. Enroll free to practise them all.