Packing and Covering Immersion Models of Planar Subcubic Graphs

  • Archontia C. Giannopoulou
  • O-joung Kwon
  • Jean-Florent Raymond
  • Dimitrios M. Thilikos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9941)


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(kh) vertices/edges such that \(G\setminus F\) does not contain H as an immersion.


Erdö–Pósa properties Graph immersions Packings and coverings in graphs 


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Copyright information

© Springer-Verlag GmbH Germany 2016

Authors and Affiliations

  • Archontia C. Giannopoulou
    • 1
  • O-joung Kwon
    • 2
  • Jean-Florent Raymond
    • 3
    • 5
  • Dimitrios M. Thilikos
    • 3
    • 4
  1. 1.Technische Universität BerlinBerlinGermany
  2. 2.Institute for Computer Science and ControlHungarian Academy of SciencesBudapestHungary
  3. 3.AlGCo Project-TeamCNRS, LIRMMMontpellierFrance
  4. 4.Department of MathematicsNational and Kapodistrian University of AthensAthensGreece
  5. 5.University of WarsawWarsawPoland

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