King Arthur expects 150 knights for an annual dinner at Camelot. Unfortunately, some of the knights quarrel with each other, and Arthur knows who quarrels with whom. Arthur wants to seat his guests around a table so that no two quarreling knights sit next to each other.
a. Which standard problem can be used to model King Arthur's task?
b. As a research project, find a proof that Arthur's problem has a solution if each knight does not quarrel with at least 75 other knights.