Getting GitHub repository information by different criteria
My limited understanding, based on brief browsing GitHub API documentation, is that currently there is NO single API request that supports all your listed criteria at once. However, I think that you could use the following sequence in order to achieve the goal from your example (at least, I would use this approach):

1) Request information on all public repositories (API returns summary representations only): https://developer.github.com/v3/repos/#list-all-public-repositories;

2) Loop through the list of all public repositories retrieved in step 1, requesting individual resources, and save it as new (detailed) list (this returns detailed representations, in other words, all attributes): https://developer.github.com/v3/repos/#get;

3) Loop through the detailed list of all repositories, filtering corresponding fields by your criteria. For your example request, you'd be interested in the following attributes of the parent object: stargazers_count, forks_count. In order to filter the repositories by number of committers, you could use a separate API: https://developer.github.com/v3/repos/#list-contributors.

Updates or comments from people more familiar with GitHub API are welcome!