, a digraph is a handle decomposition in which all handles have length in A. Note that an A-ear-decomposition (resp. A-handle-decomposition) of a graph (resp. digraph) can be seen as an ear decomposition (resp. handle decomposition) with no ear (resp. handle) with length in A. In view of all our results

, A-Ear-Decomposition Input: A graph G. Question: Does G admit an A-ear-decomposition ?

A. , Question: Does D admit an A-handle-decomposition ? It would be nice to characterize the graphs (resp. digraphs) for which A-Ear-Decomposition (resp. A-Handle-Decomposition) is polynomial-time solvable. Below is an easy lemma, Decomposition Input: A digraph D

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