Abstract
A digraph G immerses a digraph H if there is an injection f: V(H) → V(G) and a collection of pairwise edge-disjoint directed paths Puv, for uv ∈ E(H), such that Puv starts at f(u) and ends at f(v). We prove that every Eulerian digraph with minimum out-degree t immerses a complete digraph on Ω(t) vertices, thus answering a question of DeVos, McDonald, Mohar and Scheide.
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Acknowledgement
We would like to thank Paul Wollan for an insightful conversation on the topic of immersions.
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Supported by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC-2181/1 - 390900948 (the Heidelberg STRUCTURES Cluster of Excellence) and by EPSRC grant EP/V007327/1.
Research supported by the Royal Society.
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Girão, A., Letzter, S. Immersion of complete digraphs in Eulerian digraphs. Isr. J. Math. (2023). https://doi.org/10.1007/s11856-023-2572-y
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DOI: https://doi.org/10.1007/s11856-023-2572-y