A -cycle on a graph is a function such that for each edge ,
both and are circulations on . For an oriented cycle and an edge of , define if traverses in forward direction, and if traverses in backward direction. Then examples of -cycles are: take two vertex-disjoint oriented cycles and of and define . Also on each - and -subdivision are -cycles. In this talk, we show that each -cycle on can be written as a sum of four types of special -cycles.
This is joint work with Serguei Norine and Robin Thomas.