There are two approaches, using the github search api or a few calls to their other apis (explained below).
Either way, just look through their docs. I looked through their docs for a few minutes and found all this stuff. It'll probably help you a lot if you look too.
First get the name of all the public repositories (docs):
GET /repositories
And then for each repository you can get the tree (docs):
GET /repos/:owner/:repo/git/trees/:sha
Which will return something like this:
{
"sha": "9fb037999f264ba9a7fc6274d15fa3ae2ab98312",
"url": "https://api.github.com/repos/octocat/Hello-World/trees/9fb037999f264ba9a7fc6274d15fa3ae2ab98312",
"tree": [
{
"path": "file.rb",
"mode": "100644",
"type": "blob",
"size": 30,
"sha": "44b4fc6d56897b048c772eb4087f854f46256132",
"url": "https://api.github.com/repos/octocat/Hello-World/git/blobs/44b4fc6d56897b048c772eb4087f854f46256132"
},
{
"path": "subdir",
"mode": "040000",
"type": "tree",
"sha": "f484d249c660418515fb01c2b9662073663c242e",
"url": "https://api.github.com/repos/octocat/Hello-World/git/blobs/f484d249c660418515fb01c2b9662073663c242e"
},
{
"path": "exec_file",
"mode": "100755",
"type": "blob",
"size": 75,
"sha": "45b983be36b73c0788dc9cbcb76cbb80fc7bb057",
"url": "https://api.github.com/repos/octocat/Hello-World/git/blobs/45b983be36b73c0788dc9cbcb76cbb80fc7bb057"
}
]
}
And then you can check each path to see if it contains pom.xml