4. An edge e can be (x) always full, (y) sometimes full,(z) never full; it can be (x') always crossing, (y') sometimes crossing, (z') never crossing. So there are nine possible combinations: (xx') always full and always crossing, (xy) always full and sometimes crossing, and so on. Or are there? Maybe some possibilities are impossible. Let's draw a table: The edge e is: always full sometimes full never full Possible Possible always crossing f:2 or or S e: 1 impossible? impossible? Possible Possible sometimes crossing f:1 or or 8 e: 1 impossible? impossible? Possible Possible Possible never crossing or or or impossible? impossible? impossible? Take a piece of paper, complete the 3 × 3 table below by either finding an example illustrating that the combination is possible or by concluding that it is impossible. To do so, you will need the Max Flow Min Cut Theorem plus a bit of your own thinking. Once you have completed the table, select which of the following statements are true: There is a flow network and an edge e that is...

4. An edge e can be (x) always full, (y) sometimes full,(z) never full; it can be (x') always crossing, (y') sometimes crossing, (z') never crossing. So there are nine possible combinations: (xx') always full and always crossing, (xy) always full and sometimes crossing, and so on. Or are there? Maybe some possibilities are impossible. Let's draw a table: The edge e is: always full sometimes full never full Possible Possible always crossing f:2 or or S e: 1 impossible? impossible? Possible Possible sometimes crossing f:1 or or 8 e: 1 impossible? impossible? Possible Possible Possible never crossing or or or impossible? impossible? impossible? Take a piece of paper, complete the 3 × 3 table below by either finding an example illustrating that the combination is possible or by concluding that it is impossible. To do so, you will need the Max Flow Min Cut Theorem plus a bit of your own thinking. Once you have completed the table, select which of the following statements are true: There is a flow network and an edge e that is...