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Hall sMarriageTheoremassertsthatabipartitegraphG = V , U , Ehasa matching that matchesall vertices of the set V if andonlyif for eachsubset S V , | R

HallsMarriageTheoremassertsthatabipartitegraphG=V,U,Ehasa
matching that matchesall vertices of the set V if andonlyif for eachsubset
S V,|R(S)|>=|S|whereR(S)isthesetofallvertices adjacent to a vertex
in S. Check this property for the following graph with (i) V ={1,2,3,4}
and (ii) V ={5,6,7}.
1234
567
b. You have to devise an algorithm that returns yes if there is a matching in
a bipartite graph G =V,U,E that matches all vertices in V and returns
no otherwise. Would you base your algorithm on checking the condition
of Halls Marriage Theorem?

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