COMBINATORIAL APPROACHES TO MULTIFLOW PROBLEMS.

The author presents some methods and results recently discovered in the theory of network flows. He considers classes of more or less traditional problems arising in connection with families of flows sharing capacities of the same network. Such families, usually known as 'multicommodity network flows', are referred to as multiflows. Only non-directed networks are considered. Moreover, the treatment is confined to situations which are 'linear' in the sense that only linear constraints and objectives are considered for multiflow problems, and only real-valued solutions are being sought. Nevertheless, the author is particularly interested in integral, 'half-' and 'quarter-integral' solutions whenever they exist - but only due to the nature of the problem and the method it is handled with.