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Excluding Graphs as Immersions in Surface Embedded Graphs

Abstract : We prove a structural characterization of graphs that forbid a fixed graph $H$ as an immersion and can be embedded in a surface of Euler genus $\gamma$. In particular, we prove that a graph $G$ that excludes some connected graph $H$ as an immersion and is embedded in a surface of Euler genus $\gamma$ has either "small" treewidth (bounded by a function of $H$ and $\gamma$) or "small" edge connectivity (bounded by the maximum degree of $H$). Using the same techniques we also prove an excluded grid theorem on bounded genus graphs for the immersion relation.
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Preprints, Working Papers, ...
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00805139
Contributor : Dimitrios Thilikos <>
Submitted on : Wednesday, March 27, 2013 - 10:56:18 AM
Last modification on : Thursday, November 26, 2020 - 3:50:03 PM

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  • HAL Id : lirmm-00805139, version 1
  • ARXIV : 1303.6567

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Archontia C. Giannopoulou, Marcin Kaminski, Dimitrios M. Thilikos. Excluding Graphs as Immersions in Surface Embedded Graphs. 2013. ⟨lirmm-00805139⟩

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