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This is a basic question… but I’m thinking that O(M+N) is the same as O(max(M,N)), since the larger term should dominate as we go to infinity? Also, that would be different from O(min(M,N)), is that right? I keep seeing this notation, esp. when discussing graph algorithms. For example, you routinely see: O(|V| + |E|) (e.g., http://algs4.cs.princeton.edu/41undirected/).
Yes, O(M+N) means the same thing as O(max(M, N)). That is different than O(min(M, N)). As @Dr_Asik says, O(M+N) is technically linear O(N) but when M and N have a meaning, it is nice to be able to say “linear in what?” Imagine the algorithm is linear in the number of rows and the number of columns. We can either define N = rows + cols and say O(N) or we can say O(M+N) where M is rows and N is columns.