You don't need to specify the minimum versions but you should be focusing on the better performing dependencies. Always keep this in mind.
If minimal means the number of dependencies, you can use a package such as pipdeptree which shows the dependency tree of installed libraries in your environment. You can just list the top level libraries in your requirements and the other dependencies will be installed alongside with those top libraries.
When you install that library and just type pipdeptree you will see a similar output as below:
python-gitlab==1.8.0
- requests [required: >=2.4.2, installed: 2.22.0]
- certifi [required: >=2017.4.17, installed: 2019.6.16]
- chardet [required: >=3.0.2,<3.1.0, installed: 3.0.4]
- idna [required: >=2.5,<2.9, installed: 2.8]
- urllib3 [required: >=1.21.1,<1.26,!=1.25.1,!=1.25.0, installed: 1.25.3]
- six [required: Any, installed: 1.11.0]
python-jenkins==1.7.0
- multi-key-dict [required: Any, installed: 2.0.3]
- pbr [required: >=0.8.2, installed: 1.10.0]
- requests [required: Any, installed: 2.22.0]
- certifi [required: >=2017.4.17, installed: 2019.6.16]
- chardet [required: >=3.0.2,<3.1.0, installed: 3.0.4]
- idna [required: >=2.5,<2.9, installed: 2.8]
- urllib3 [required: >=1.21.1,<1.26,!=1.25.1,!=1.25.0, installed: 1.25.3]
- six [required: >=1.3.0, installed: 1.11.0]
So your requirements can be something like:
python-gitlab==1.8.0
python-jenkins==1.7.0
If you meant to specify the minimum possible versions then I don't know.