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. © 2013 Springer-Verlag.
CITATION STYLE
Giannopoulou, A. C., Kamiński, M., & Thilikos, D. M. (2013). Excluding graphs as immersions in surface embedded graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8165 LNCS, pp. 274–285). Springer Verlag. https://doi.org/10.1007/978-3-642-45043-3_24
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