Prove theorem 1 as a corollary of theorem 2

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Reference no: EM131168797

Prove Theorem 1 as a corollary of Theorem 2.

Hint: look at the conditions for whether the current flow of zero on edge e is maximum.

Theorem 1

Consider any maximum cardinality matching of a graph G and an edge e that does not belong to the matching. Then e belongs to some maximum cardinality matching if any only if it is part of (a) an alternating cycle, or (b) an even alternating path, one end of which is a vertex that is incident to no edge in the matching.

Theorem 2
A given feasible flow f on a graph maximizes the flow on (i, j) if and only if there is no augmenting path from j to i in the residual graph R(f).

Reference no: EM131168797

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