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Auteurs principaux:	Lu, Junying, Chen, Yaojun
Format:	Preprint
Publié:	2025
Sujets:	Combinatorics 05C20
Accès en ligne:	https://arxiv.org/abs/2509.17756
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author	Lu, Junying Chen, Yaojun
author_facet	Lu, Junying Chen, Yaojun
contents	The girth of a graph $G$ is the length of a shortest cycle of $G$. Jiang (JCT-B, 2001) showed that every graph $G$ with girth at least $2\ell+1$ and minimum degree at least $k/\ell$ contains every tree $T$ with $k$ edges whose maximum degree does not exceed the minimum degree of $G$. Let $δ^0(D)$ be the minimum semidegree of a digraph $D$ and $Δ(D)$ be the maximum degree of $D$. In this paper, we establish a digraph version of Jiang's result, stating that every oriented graph $D$ of girth at least $2\ell+1$ with $δ^0(D)\ge \max\{k/\ell,Δ(T)\}$ contains every oriented tree with $k$ edges, that answers a question raised by Stein and Trujillo-Negrete in affirmative.
format	Preprint
id	arxiv_https___arxiv_org_abs_2509_17756
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Oriented trees in digraphs with large girth Lu, Junying Chen, Yaojun Combinatorics 05C20 The girth of a graph $G$ is the length of a shortest cycle of $G$. Jiang (JCT-B, 2001) showed that every graph $G$ with girth at least $2\ell+1$ and minimum degree at least $k/\ell$ contains every tree $T$ with $k$ edges whose maximum degree does not exceed the minimum degree of $G$. Let $δ^0(D)$ be the minimum semidegree of a digraph $D$ and $Δ(D)$ be the maximum degree of $D$. In this paper, we establish a digraph version of Jiang's result, stating that every oriented graph $D$ of girth at least $2\ell+1$ with $δ^0(D)\ge \max\{k/\ell,Δ(T)\}$ contains every oriented tree with $k$ edges, that answers a question raised by Stein and Trujillo-Negrete in affirmative.
title	Oriented trees in digraphs with large girth
topic	Combinatorics 05C20
url	https://arxiv.org/abs/2509.17756

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// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

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