I want to organize a business lunch with two societies $E_1$ (mine) and $E_2$. Each society is made of four people from the Executive management and 6 of the Financial Management. I want to organize this lunch with two tables of ten people with the following constraints :
- At least one member of each four department has to be on each table
- At most three people of each department can sit together at a table
- At least three people of each Executive management department have to be at the table $1$.
I did the following graph :
And applied Ford-Fulkerson (I'm not sure on how to apply it, the itreation are in parenthesis $(number \ of \ the \ iteration)$ ):
The thing is that I'm not able to let everybody sit ... I have only 8 people from society 2. Do I have too much constraints or did I did a mistake ?
What would be the minimum cut ? Is there a minimum cut if I don't have a maximal stream ? Would it verify the Ford-Fulkerson theorem ?