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Hall's Marriage Theorem

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Bipartite graph with every left vertex connected to exactly two right vertices

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Existence of a perfect matching

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A team-based bipartite graph where each team needs to pick a unique meeting room, but some rooms are too small for certain teams

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Existence of a perfect matching

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A bipartite graph where left vertices are tasks and right vertices are workers, each task can be done by at least one worker

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Existence of a perfect matching

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Matching courses to students in a bipartite graph where every course is liked by at least one student

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Existence of a perfect matching

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A bipartite graph with left vertices representing students and right vertices representing desks, where each student likes exactly 3 desks

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Existence of a perfect matching

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Family gathering scenario modeled as a bipartite graph with members and seats, where each member has a list of preferred seats

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Existence of a perfect matching

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A bipartite graph where each right vertex has a degree of 1

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Existence of a perfect matching

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Bipartite graph representing job assignments with all jobs requiring a unique skill

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Existence of a perfect matching

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