"The end of major hostilities" ?
What are you imagining that this means?

I believe you have made a mistake and what you meant to say is the end of major combat operations.
And to answer this question. The answer is no.
To give an example: the invasion of Normandy could be called a major combat operation. And say when you got to the stage of using other seaports to ship in war material and longer longer needed the beachheads that were established for the Normandy invasion, you could then declare that this was the end of this major combat operation.
And if you were talking to the naval people who were conducting this operation you could say it was the end of *the* major combat operations and that their mission was successfully accomplished.

Now, this is a very simple concept, but those who were against the war are suffering from similar thing as PEST- when people are dazed and confused they can think and say many silly things. But be forewarned that when the elections occur in Iraq on Jan 30, this again will also cause a similar condition as PEST.