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In model of bipartite graph in computer networks

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Question

In a model of a bipartite graph in computer networks, there are 12 servers and 15 clients. Each client needs to be connected to exactly 2 servers for optimal performance. Is it possible to connect each client to 2 servers in such a way that no server is overloaded, i.e., each server has at most 4 clients connected to it? Hint: You can use Hall's Marriage Problem to solve this.

Hall's Marriage Theorem:

Suppose G is a bipartite graph with bipartition (A,B). There is a matching that covers A if and only if for every subset X ⊆ A, N(X) ≥ |X| where N(X) is the number of neighbours of X.

Reference no: EM133466862

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