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Bibliographic Details
Main Authors:	Wu, Di, Wu, Rong
Format:	Preprint
Published:	2023
Subjects:	Combinatorics
Online Access:	https://arxiv.org/abs/2306.12062
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On Borodin-Kostochka conjecture for correspondence coloring
by: Dvořák, Zdeněk, et al.
Published: (2026)

Coloring some $(P_6,C_4)$-free graphs with $Δ-1$ colors
by: Chen, Ran, et al.
Published: (2024)

On a conjecture of Tokushige for cross-$t$-intersecting families
by: Zhang, Huajun, et al.
Published: (2024)

Cover-free families on graphs
by: Parida, Prangya, et al.
Published: (2026)

Structure and coloring of a family of ($P_7, C_5$)-free graphs
by: Chen, Ran, et al.
Published: (2023)

Proof of Frankl's conjecture on cross-intersecting families
by: Wu, Yongjiang, et al.
Published: (2024)

The perfect divisibility and chromatic number of some odd hole-free graphs
by: He, Weihua, et al.
Published: (2026)

Trisimplicial vertices in (fork, odd parachute)-free graphs
by: Lan, Kaiyang, et al.
Published: (2025)

Seymour and Woodall's conjecture holds for graphs with independence number two
by: Chen, Rong, et al.
Published: (2024)

On conflict-free colorings of cyclic polytopes and the girth conjecture for graphs
by: Lee, Seunghun, et al.
Published: (2024)

Characterization of $P_3$-connected graphs
by: Chen, Rong
Published: (2025)

Optimal $χ$-boundness of $\ell$-holed graphs
by: Wang, Yan, et al.
Published: (2025)

Equivalent formulation of Thomassen's conjecture using Tutte paths in claw-free graphs
by: Kabela, Adam, et al.
Published: (2019)

The class of $(2P_3,C_4,C_6)$-free graphs, part II: $(2P_3,C_4,C_6,C_7,T_0)$-free graphs
by: Penev, Irena
Published: (2025)

There are finitely many $5$-vertex-critical $(P_6,\text{bull})$-free graphs
by: Ju, Yiao, et al.
Published: (2025)

On supratopologies, normalized families and Frankl conjecture
by: Carvalho, André, et al.
Published: (2024)

Proof of a conjecture on graph polytope
by: Liu, Feihu
Published: (2024)

The class of $(2P_3,C_4,C_6)$-free graphs, part I: $(2P_3,C_4,C_6)$-free graphs that contain an induced $C_7$ or an induced $T_0$
by: Penev, Irena
Published: (2025)

Coloring of some $(P_2\cup P_4)$-free graphs
by: Ran, Chen, et al.
Published: (2024)

4K_1 free graphs on 13 vertices have cop number at most 2
by: Wu, Zhaoyu
Published: (2026)

Around the positive graph conjecture
by: Conlon, David, et al.
Published: (2024)

On Kotzig's conjecture in random graphs
by: Glock, Stefan, et al.
Published: (2025)

On degree power sum in $P_k$-free graphs
by: Ai, Jiangdong, et al.
Published: (2024)

Vertex-critical $(P_5,\text{chair})$-free and $(P_5,\text{cricket})$-free graphs
by: Jooken, Jorik
Published: (2026)

Spectral extremal graphs for $F_6$-free graphs with even size
by: Yu, Loujun, et al.
Published: (2025)

Proof of a conjecture on eigenvalues of transposition graph
by: Ku, Cheng Yeaw, et al.
Published: (2025)

An infinite family of counterexamples to a conjecture on distance magic labeling
by: Ebrahem, Ehab, et al.
Published: (2024)

Edge density and minimum degree thresholds for $H$-free graphs with unbounded chromatic number
by: Wu, Zhuo, et al.
Published: (2025)

Hamiltonian cycles in tough $(P_4 \cup P_1)$-free graphs
by: Shan, Songling
Published: (2025)

Non-empty intersection of longest paths in $P_5$-free and claw-free graphs
by: Lima, Paloma T., et al.
Published: (2024)

Secure domination in $P_5$-free graphs
by: Gupta, Uttam K., et al.
Published: (2025)

Vu's conjecture holds for claw-free graphs
by: Cook, Linda, et al.
Published: (2025)

Some conjectures on $r$-graphs and equivalences
by: Ma, Yulai, et al.
Published: (2024)

The linear Turán number of the 3-graph $P_5$
by: Tang, Chaoliang, et al.
Published: (2026)

Reconfiguration graphs for vertex colorings of $P_5$-free graphs
by: Lei, Hui, et al.
Published: (2024)

A counterexample to Hickingbotham's conjecture about $k$-ghost-edges
by: Chen, Rong
Published: (2026)

Jones' conjecture for Halin graphs and a bit more
by: Bärnkopf, Pál, et al.
Published: (2024)

Combinatorial data of a free arrangement and the Terao conjecture
by: Cong, Tran Quoc
Published: (2013)

Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs
by: Shan, Songling, et al.
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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