discrete structure

Part II: Graph Modelling

Question

Suppose that there are five young women and six young men on an island. Each woman is willing to marry some of the men on the island and each man is willing to marry any woman

who is willing to marry him. Suppose that Ana is willing to marry Jason, Larry, and Matt; Barbara is willing to marry Kevin and Larry; Carol is willing to marry Jason, Nick and Oscar; Diane is willing to marry Jason, Larry, Nick and Oscar; Elizabeth is willing to marry Jason and Matt.

Model the possible marriage on the island using a bipartite graph.

Find a matching of the young women and the young men on the island such that each young woman is matched with a young man whom she is willing to marry.