Unit $14$ Assignment

Start with the following arbitrary matching $($thick red lines$)$ in a bipartite graph. Find an augmenting path and the resulting maximum matching.

In the following graph, all the edges have capacity equal to one.

$($a$)$ For the given flow from $s$ to $t,$ draw the residual network.

$($b$)$ Is it possible to increase the network flow? If so$,$ show the augmenting path and the final $($maximum$)$ network flow. If it is not possible to increase the network flow, then explain why not.