Let G be an eulerian graph. For each vertex v∈ V (G), let T (v) be a non-empty subset of a
partition of the edges incident with v into 2-subsets and set T=∪ v∈ V (G) T (v), called a
transition system of G. A transition system T of G is admissible if T∩ F|≤ 1 2| F| for every T∈
T and every edge cut F of G. A cycle decomposition C of G is called a compatible cycle
decomposition (CCD for short) of (G, T) if| E (C)∩ T|≤ 1 for every cycle C∈ C and every T∈
TH Fleischner proved that if G is planar, then for every admissible transition system T of …