Marx, Dániel and Wollan, P (2014) Immersions in highly edge connected graphs. SIAM JOURNAL ON DISCRETE MATHEMATICS, 28 (1). pp. 503-520. ISSN 0895-4801 10.1137/130924056

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Abstract

We consider the problem of how much edge connectivity is necessary to force a graph G to contain a fixed graph H as an immersion. We show that if the maximum degree in H is δ, then all the examples of δ-edge connected graphs which do not contain H as a weak immersion must have a treelike decomposition called a tree-cut decomposition of bounded width. If we consider strong immersions, then it is easy to see that there are arbitrarily highly edge connected graphs which do not contain a fixed clique Kt as a strong immersion. We give a structure theorem which roughly characterizes those highly edge connected graphs which do not contain Kt as a strong immersion. © 2014 Society for Industrial and Applied Mathematics.

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