Packing and covering immersion-expansions of planar sub-cubic graphs. (October 2017) - Giannopoulou, Archontia C.; Kwon, O-joung; Raymond, Jean-Florent; Thilikos, Dimitrios M.
Abstract: A graph H is an immersion of a graph G if H can be obtained by some subgraph G after lifting incident edges. We prove that there is a polynomial function f : N × N → N, such that if H is a connected planar sub-cubic graph on h > 0 edges, G is a graph, and k is a non-negative integer, then either G contains k vertex/edge-disjoint subgraphs, each containing H as an immersion, or G contains a set F of f ( k, h ) vertices/edges such that G ∖ F does not contain H as an immersion.