To add a public GitHub repository to your project using Composer, you can follow these steps:

1. Open the composer.json file in your Laravel project.
2. Add the GitHub repository as a dependency in the repositories section of composer file. If repository includes a composer.json file, you can directly require the package using its name and version. Otherwise, you can specify the repository URL directly.

Here's an example of how to add a public GitHub repository in your composer.json:

{
  "repositories": [
    {
      "type": "vcs",
      "url": "https://github.com/username/repository-name"
    }
  ],
  "require": {
    "username/repository-name": "dev-master"
  }
}

Replace "username" with the GitHub username of the repository owner and "repository-name" with the name of the repository.

3. After adding the repository and package to the composer.json file, run the following Composer command in your terminal to install the package:

composer install

This will fetch and install the package from the public GitHub repository into your Laravel project.

Please ensure that you have the necessary permissions to access the public GitHub repository and that the repository is publicly accessible.