Dna paternity testing has become the most widely accepted method for establishing who the father of a child is when there are doubts. in one case the mother refused to supply a sample of her dna, but the man claiming to be the father had his dna and that of the baby's taken and analyzed. is it possible to establish who the father is in this method even if the mother's dna is not available to compare?

Solely by this method, it is not possible. Several other additional DNA testing must be preformed if there isn't the mother's DNA.
The mother's DNA serves to make sure that all the resulting parts from the father's DNA can be completed by the mother's DNA when matching it all with the child's DNA. For this method, the child's DNA is "cut" in specific sites by restriction enzymes. This restriction enzymes are put to "cut" also the mother's DNA and the father's DNA. It is expected that all the resulting segments from the child's DNA can be found either on the mother's side or the father's side. All segments that can be matched to the mother's DNA segments, should be matched to the father's DNA segments. That's why the mother's DNA is so important for this method.