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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 γ. 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 γ has either “small” treewidth (bounded by a function of H and γ) 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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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01483644
Contributor : Dimitrios Thilikos <>
Submitted on : Monday, March 6, 2017 - 11:35:21 AM
Last modification on : Monday, June 8, 2020 - 9:48:02 AM

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Archontia C. Giannopoulou, Marcin Kamiński, Dimitrios M. Thilikos. Excluding Graphs as Immersions in Surface Embedded Graphs. WG: Workshop on Graph-Theoretic Concepts in Computer Science, Jun 2013, Lübeck, Germany. pp.274-285, ⟨10.1007/978-3-642-45043-3_24⟩. ⟨lirmm-01483644⟩

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