How to present a parliament opposition in graph theory. My teacher asked us this question to think about. It is not a homework question. The question: There is a parliament where every member of parliament (MP) has three opposition. If the parliament split to two parts such that every MP has only one opposition. How to present this in graph theory?

I am just going to give a hint so that your teacher's "think" will serve it's purpose. In the first case, make each member of parliament as a node and then draw edges between him and opposition members. It will be a n-regular graph depending on the number of oppositions which in this is case is 3. Then keep removing edges such that one member has only one edge. Draw a simple 3-regular graph and remove edges and see how this will turn out to be.