The structure of graphs with no K3,3 immersion
Matt DeVos, Mahdieh Malekian · Journal of Graph Theory · 2021
Abstract The Kuratowski–Wagner Theorem asserts that a graph is planar if and only if it does not have either or as a minor. Using this, Wagner obtained a precise description of all graphs with no ‐minor and all graphs with no ‐minor. Similar results have been achieved for the class of graphs with no ‐minor for a number of small graphs . In this paper we give a precise structure theorem for graphs which do not contain as an immersion. This strengthens an earlier theorem of Giannopoulou, Kamiński, and Thilikos that gives a rough description of the class of graphs with no or immersion.