1) The Munich Analogy,
2) The “lessons of Vietnam” (and/or the “Vietnam Analogy),
3) the Thucydides Trap. Your essay should at least briefly show that you understand these three concepts. It is OK to make major use of one or more of these concepts in the analytical structure of your essay, and it is also OK to say that one or more of them, or that all three of them, are basically irrelevant to U.S.-China relations. In other words, the assignment does not require you to apply any of these concepts to U.S.- China relations – it’s OK to argue that none of them apply.
It’s also OK to argue that one or two or all three of them are somewhat relevant, or highly relevant, in analyzing U.S.-China relations. The only requirement is that you mention them and demonstrate that you understand the three concepts. Beyond that, you can say whatever you wish to about U.S.-China relations. It is OK to primarily focus on security, military and geopolitical aspects, and it is also OK to focus mainly on economic aspects, or even to focus on social and person-to-person aspects. The theme and main points of your essay are totally up to you so long as you include some discussion of these three items.