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 \(f:{\mathbb {N}}\times {\mathbb {N}}\rightarrow {\mathbb {N}}\), such that if H is a connected planar subcubic 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 \(G\setminus F\) does not contain H as an immersion.
The original version of this chapter was revised: The affiliation of the author has been corrected. The erratum to this chapter is available at 10.1007/978-3-662-53536-3_26
A.C. Giannopoulou—The research of this author has been supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC consolidator grant DISTRUCT, agreement No 648527) and by the Warsaw Center of Mathematics and Computer Science.
O.-j. Kwon—Supported by ERC Starting Grant PARAMTIGHT (No. 280152)
J.-F. Raymond—Supported by the (Polish) National Science Centre grant PRELUDIUM 2013/11/N/ST6/02706.
An erratum to this chapter can be found at http://dx.doi.org/10.1007/978-3-662-53536-3_26
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Notes
- 1.
While we mentioned this definition in the introduction, we now adopt the more technical definition of immersion in terms of immersion models as this will facilitate the presentation of the proofs.
- 2.
All proofs with a \((\star )\) have been omitted from this extended abstract.
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Giannopoulou, A.C., Kwon, Oj., Raymond, JF., Thilikos, D.M. (2016). Packing and Covering Immersion Models of Planar Subcubic Graphs. In: Heggernes, P. (eds) Graph-Theoretic Concepts in Computer Science. WG 2016. Lecture Notes in Computer Science(), vol 9941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53536-3_7
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