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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define a bipartite graph.
💡 Hint: Think about how the vertices are organized in two distinct groups.
Question 2
Easy
What is Hall's Marriage Theorem?
💡 Hint: Consider its application in matching problems.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What ensures a complete matching exists in a bipartite graph?
- Only the number of vertices
- The number of neighbors and vertices must be equal or greater
- The edges formed randomly
💡 Hint: Think about the relationship between vertices in different sets.
Question 2
Hall's Marriage Theorem applies to which type of graphs?
- True
- False
💡 Hint: Recall the definition of a bipartite graph.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a bipartite graph with 6 vertices in V₁ and 8 in V₂, five vertices in V₁ have enough neighbors in V₂ to meet Hall's condition, one does not, and one vertex in V₂ is left unmatched. Can a complete matching still be formed?
💡 Hint: Evaluate the matching possibility based on the violating vertex.
Question 2
Create an example of a bipartite graph that satisfies Hall's condition and show how to build a complete matching.
💡 Hint: Draw the graph to visualize connections.
Challenge and get performance evaluation