(c) State and prove Hall’s Theorem

Hall’s Theorem is a fundamental result in combinatorics and graph theory, specifically in the context of bipartite graphs. It provides a necessary and sufficient condition for the existence of a perfect matching in a bipartite graph.

Hall’s Theorem:

Let G=(X,Y,E)G = (X, Y, E) be a bipartite graph where XX and YY are disjoint sets of vertices, and EE is the set of edges between _______ ______ _____ ____ _________ _____ ________ _______ ___ ______.
_____ ____ ________ __________ ________ ___ _____ ____ _____ ____ _______ ________.
__________ ____ _________ ____ _____ ______ ___.
__________ _____ _______ __________ ________ ___ ______ __________ _____ ______ ________ ________.
______ _________ __________ _______ ___ _____.
_______ __________ ___ ___ __________ __________.
_________ __________ __________ _________ _____ ___ ________ _________ __________ __________ _____.
_______ ______ ________ ___ ________ _______ ___ ________.
____ ________ _____ ____ ______ ____ ________ ___ __________.
______ ____ __________ _____ __________ _________ _______ ______.
________ _______ ______ __________ _________ _______ __________ ________ _________ _______.
______ ______ _______ ___ _______ ______ __________ ________ ____ ______ _______ ____.
_______ _____ __________ ___ ________ ______ _____ __________ ________ ______ __________.
________ _______ _______ ___ _______ _______ ______ ______ ________.
_________ _____ _________ _____ ___ ____ ______ ____ ______ ____ ____.
___ __________ ___ _____ __________ ___ _________ _____ __________ _____ ___ __________.
__________ _________ ______ ______ ______ _____ _____ _____ ______ _____ _____ _______.
_______ ______ _________ ____ ______ _________ ______ ________ __________ _______ _____.
______ ________ ____ _____ ____ _______ __________ ___ __________ ______.
________ ___ ___ _____ ___ ______ ____ ___ __________.
Get Full Answer on WhatsApp