Obstacles to Partitioning a Graph into Trees

We formulate a class of combinatorial problems about the trees of a graph, which arise in connection with algorithms processing group requests to transmit information in a network. The problem of polar packing of reciprocal trees is solved. A conjecture of minimal partitioning of a graph into trees is stated and justified. A lower bound is established on the number of trees into which a graph can be partitioned. A technique for partitioning a graph into trees is developed. This tech-technique is applied to prove the conjecture for one class of graphs.