The structure of graphs with no K3,3 immersion

The Kuratowski–Wagner Theorem asserts that a graph is planar if and only it does not have either K 3 , or 5 as minor. Using this, Wagner obtained precise description of all graphs with no -minor -minor. Similar results been achieved for the class H number small . In this paper we give structure theorem which do contain an immersion. This strengthens earlier Giannopoulou, Kamiński, Thilikos gives rough