Practice - Necessary and Sufficient Condition for Complete Matching
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Practice Questions
Test your understanding with targeted questions
Define a bipartite graph.
💡 Hint: Think about the two distinct groups in the graph.
What does matching mean in the context of graphs?
💡 Hint: Consider how you could pair up objects without overlap.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is a bipartite graph?
💡 Hint: Consider the definition and how vertices are arranged.
True or False: A complete matching always exists in every bipartite graph.
💡 Hint: Think about conditions necessary for complete matching.
1 more question available
Challenge Problems
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Given a bipartite graph with subsets U={1, 2, 3} and V={a, b} where U has preferences: 1-a, 1-b, 2-a, 3-a, determine if complete matching is possible.
💡 Hint: Use Hall's theorem to check against preferences.
In a graph representing students to projects, students S={X, Y} can do projects P={1, 2, 3}. X can do 1 & 2, Y can do 2 & 3. Is there complete matching?
💡 Hint: Analyze the connections using Hall's theorem conditions.
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