Maximizing the number of independent subsets over trees with maximum degree 3

The present disclosed invention includes a telephone set provided with a facsimile function. The telephone set includes an image reader which can be mounted on and detached from its body. The reader can be detached and operated to scan an original with an image to be transmitted thereon. A read-out image data signal is modulated in frequency and then transmitted toward a receiving portion in the body through a transmitting portion in the reader. The received image data are transmitted to another desired facsimile terminal equipment through a telephone line. Since there is no need for an electric wire to be connected between the body and the reader, a more flexible reading of an image can be achieved.