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arXiv · 2108.13959

Immersion of complete digraphs in Eulerian digraphs

António Girão·Shoham Letzter
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Abstract

A digraph $G$ \emph{immerses} a digraph $H$ if there is an injection $f : V(H) \to V(G)$ and a collection of pairwise edge-disjoint directed paths $P_{uv}$, for $uv \in E(H)$, such that $P_{uv}$ starts at $u$ and ends at $v$. 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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António Girão, Shoham Letzter. 2022-04-11. Immersion of complete digraphs in Eulerian digraphs. https://arxiv.org/abs/2108.13959

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