def path_in_cc(path, cc):
    """Determines whether all vertices of a given path belong to a given
    connected component.

    :param path:
    :param cc: list of vertices representing a connected component in a graph
    :return: True if the path vertices are found in the connected component,
        False otherwise
    """
    for node in path:
        if node not in cc:
            return False
    return True