For a machine learning problem, how do I theoretically calculate the maximum number of support vectors required to solve the machine learning problem ?
The maximum number of support vectors is the total number of examples. If you run your SVM software and find that all examples are support vectors, it means that your classifier is maximally overfitted to the data, hence will generalize poorly. The ratio of the number of support vectors to the number of examples is a simple indicator of overfitting.