The Monday lecture starts at 2:15 p.m. and lasts between 55 and 75 minutes. It is followed by a tea and coffee break, and a shorter colloquium lecture at 4:00 p.m. sharp
The lecture should address a broader audience with a background in algorithms and discrete mathematics.
An ideal lecture introduces a topic from a broader viewpoint and may proceed to more advanced and recent results. It is important to explain the setting and put the topic in a broader perspective: Why are these questions interesting or important?
You need not define what NP-completeness is, or repeat that the solution of the Traveling Salesman Problem by brute force takes more seconds than the number of hairs on your head. If you mention, for example, the complexity class FPT, or W-hardness, or Hall's theorem (the marriage theorem), or Helly's Theorem, it does no harm to remind the audience briefly in one or two sentences of the definition or of the statement, or give a few examples. On the other hand, if FPT or the marriage theorem (and its extensions) is at the core of your lecture, then a more thorough introduction can be appropriate.