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Bibliographic Details
Main Author:	Liu, Xizhi
Format:	Preprint
Published:	2025
Subjects:	Combinatorics
Online Access:	https://arxiv.org/abs/2501.19229
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Sabotage the Mantel Theorem
by: Behague, Natalie, et al.
Published: (2025)

A note on hypergraph extensions of Mantel's theorem
by: Ma, Jie, et al.
Published: (2025)

An improved hypergraph Mantel's Theorem
by: Iľkovič, Daniel, et al.
Published: (2025)

Intervals of hypergraph Turán densities
by: Liu, Xizhi, et al.
Published: (2026)

Vertex-colored Turán theorems with applications in extremal hypergraph problems
by: Chen, Wanfang, et al.
Published: (2026)

Toward a density Corrádi--Hajnal theorem for degenerate hypergraphs
by: Hou, Jianfeng, et al.
Published: (2023)

Uniquely colorable hypergraphs
by: Liu, Xizhi, et al.
Published: (2024)

Hypergraph anti-Ramsey theorems
by: Liu, Xizhi, et al.
Published: (2023)

On the boundedness of degenerate hypergraphs
by: Hou, Jianfeng, et al.
Published: (2024)

Tight bounds for rainbow partial $F$-tiling in edge-colored complete hypergraphs
by: Deng, Jinghua, et al.
Published: (2024)

Andrásfai--Erdős--Sós theorem for the generalized triangle
by: Liu, Xizhi, et al.
Published: (2024)

Andr{á}sfai--Erdős--Sós theorem under max-degree constraints
by: Liu, Xizhi, et al.
Published: (2025)

Positive codegree Andrásfai--Erdős--Sós theorem for the generalized triangle
by: Liu, Xizhi, et al.
Published: (2024)

A criterion for Andrásfai--Erdős--Sós type theorems and applications
by: Hou, Jianfeng, et al.
Published: (2024)

Density Hajnal--Szemerédi theorem for cliques of size four
by: Hou, Jianfeng, et al.
Published: (2025)

Generalized Andrásfai--Erdős--Sós theorems for odd cycles
by: Chen, Zian, et al.
Published: (2024)

Dirac's theorem for linear hypergraphs
by: Im, Seonghyuk, et al.
Published: (2024)

A hypergraph bandwidth theorem
by: Lang, Richard, et al.
Published: (2024)

Spectral generalized Turán problems
by: Liu, Xizhi
Published: (2025)

A hypergraph Heilmann--Lieb theorem
by: Wan, Jiang-Chao, et al.
Published: (2022)

Short proof of the hypergraph container theorem
by: Nenadov, Rajko, et al.
Published: (2024)

The number $4/9$ is a non-jump for $3$-graphs
by: Liu, Xizhi, et al.
Published: (2026)

A note on the minimum size of Turán systems
by: Liu, Xizhi, et al.
Published: (2025)

A generalized Turán extension of the Deza--Erdős--Frankl Theorem
by: Helliar, Charlotte, et al.
Published: (2024)

A single $3$-graph with infinite stability number
by: Li, Heng, et al.
Published: (2026)

Finite Hypergraph Families with Rich Extremal Turán Constructions via Mixing Patterns
by: Liu, Xizhi, et al.
Published: (2022)

Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods
by: Li, Heng, et al.
Published: (2026)

Strong stability from vertex-extendability and applications in generalized Turán problems
by: Chen, Wanfang, et al.
Published: (2024)

The spectral radius of $k$-chromatic $r$-graphs
by: Liu, Xizhi, et al.
Published: (2026)

Turán theorems for even cycles in random hypergraph
by: Nie, Jiaxi
Published: (2023)

Rainbow variations on a theme by Mantel: extremal problems for Gallai colouring templates
by: Falgas-Ravry, Victor, et al.
Published: (2022)

On a refinement of the Ahlswede--Katona Theorem
by: Hou, Jianfeng, et al.
Published: (2025)

A rainbow Dirac theorem for loose Hamilton cycles in hypergraphs
by: Kathapurkar, Amarja, et al.
Published: (2025)

A note on extremal constructions for the Erdős--Rademacher problem
by: Liu, Xizhi, et al.
Published: (2023)

Exact Turán number of the Fano plane in the $\ell_2$-norm
by: Hou, Jianfeng, et al.
Published: (2025)

The inducibility of Turán graphs
by: Liu, Xizhi, et al.
Published: (2026)

The spectral inducibility of graphs
by: Kang, Liying, et al.
Published: (2026)

A finite-board reduction for the Erdős Matching Conjecture and the 4-uniform case via exact certificates
by: Hou, Jianfeng, et al.
Published: (2026)

A quantitative improvement on the hypergraph Balog-Szemerédi-Gowers theorem
by: Lee, Hyunwoo
Published: (2025)

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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; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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