Practice Hall's Marriage Theorem (25.1.5) - Introduction to Bipartite Graphs and Matching
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Hall's Marriage Theorem

Practice - Hall's Marriage Theorem

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Practice Questions

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Question 1 Easy

Define a bipartite graph.

💡 Hint: Consider how edges connect the two sets.

Question 2 Easy

What is matching in a graph?

💡 Hint: Think about how edges connect vertices without overlap.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is Hall's Marriage Theorem concerned with?

The existence of cycles in graphs
Conditions for complete matching in bipartite graphs
The total number of edges in a graph

💡 Hint: Think about the relationships between vertices.

Question 2

True or False: Every maximal matching is also a maximum matching.

True
False

💡 Hint: Consider the definitions of both terms.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given a bipartite graph with sets {A, B, C} and {X, Y, Z}, where edges connect A-X, B-Y, and C-Z, devise a complete matching. What further connections can you construct to meet Hall's condition?

💡 Hint: Examine the size and distribution of edges.

Challenge 2 Hard

Consider a job assignment scenario: You have four jobs and only two employees capable of covering those roles. Why won't a complete assignment be attainable? Illustrate using Hall's theorem.

💡 Hint: Count the tasks versus available workers.

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