1 Six people, \(A , B , C , D , E\) and \(F\), are to be matched to six tasks, \(1,2,3,4,5\) and 6 .
The following adjacency matrix shows the possible matching of people to tasks.
| Task 1 | Task 2 | Task 3 | Task 4 | Task 5 | Task 6 |
| \(\boldsymbol { A }\) | 0 | 0 | 1 | 0 | 1 | 1 |
| B | 0 | 1 | 0 | 1 | 0 | 0 |
| \(\boldsymbol { C }\) | 0 | 1 | 0 | 0 | 0 | 1 |
| \(\boldsymbol { D }\) | 0 | 0 | 0 | 1 | 0 | 0 |
| \(E\) | 1 | 0 | 1 | 0 | 1 | 0 |
| \(\boldsymbol { F }\) | 0 | 0 | 0 | 1 | 1 | 0 |
- Show this information on a bipartite graph.
- Initially, \(A\) is matched to task 3, \(B\) to task 4, \(C\) to task 2 and \(E\) to task 5. From this initial matching, use the maximum matching algorithm to obtain a complete matching. List your complete matching.