Packing and covering immersion-expansions of planar sub-cubic graphs

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.
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Submitted on : Tuesday, June 12, 2018 - 4:43:20 PM
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Archontia Giannopoulou, O-Joung Kwon, Jean-Florent Raymond, Dimitrios M. Thilikos. Packing and covering immersion-expansions of planar sub-cubic graphs. European Journal of Combinatorics, Elsevier, 2017, 65, pp.154-167. ⟨10.1016/j.ejc.2017.05.009⟩. ⟨lirmm-01610005v2⟩

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