# Flow Augmenting Path Algorithm, Bipartite Graph and Cardinality

1. Find the maximum flow and the associated minimum capacity cut for the following network, by using flow augmenting path algorithm (in the order of "first labeled, first scannred"). *see attachment for diagram*

2. A maximum capacity flow augmenting path is an augmenting path such that we can increase the flow of the network by the largest amount along this path comparing to all other augmenting paths. Design a strategy (similar to the strategy of finding a shortest path) to find a maximum capacity flow augmenting path. Use your strategy to find a maximum capacity flow augmenting path for the above network with the initial 0 flow.

3. Let G={X,E,Y} be the bipartite graph as follows *see attachment*

Using flow augmenting path algorithm find a maximum cardinality matching of the above G.

https://brainmass.com/math/discrete-math/flow-augmenting-path-algorithm-bipartite-graph-and-cardinality-35717

#### Solution Summary

In this solution, we look at determining the flow and capacity from the augmenting path algorithm. Many graphs are included. This solution is neatly handwritten and attached in 5 JPG files.