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Main Authors:	Elvin, Gabriel, Gonzales, Alexis, Rodriguez, Alejandro, Wilbur, Israel
Format:	Preprint
Published:	2026
Subjects:	Combinatorics 05D10
Online Access:	https://arxiv.org/abs/2601.05442
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New Ramsey Multiplicity Bounds and Search Heuristics
by: Parczyk, Olaf, et al.
Published: (2022)

Turán Colourings in Off-Diagonal Ramsey Multiplicity
by: Hyde, Joseph, et al.
Published: (2023)

Lower Bounds for Multicolor Star-Critical Ramsey Numbers
by: Budden, Mark, et al.
Published: (2024)

Cuboids are canonically Ramsey
by: Shaw, Benedict Randall
Published: (2026)

Thresholds for constrained Ramsey and anti-Ramsey problems
by: Behague, Natalie, et al.
Published: (2024)

Ramsey numbers of trees
by: Montgomery, Richard, et al.
Published: (2025)

The Gamma-Switch Ramsey Number
by: Duffy, Christopher, et al.
Published: (2026)

Fan-complete Ramsey numbers
by: Chung, Fan, et al.
Published: (2022)

Asymmetric Ramsey numbers of trees
by: Yan, Jun
Published: (2025)

A Polynomial Ramsey Statement for Bounded VC-dimension
by: Hons, Tomáš
Published: (2025)

Canonical Ramsey numbers of sparse graphs
by: Gishboliner, Lior, et al.
Published: (2024)

Big Ramsey Degrees of Countable Ordinals
by: Boyland, Joanna, et al.
Published: (2023)

Online Ramsey numbers of ordered graphs
by: Heath, Emily, et al.
Published: (2024)

A polynomial improvement for the odd cycle-complete Ramsey numbers
by: Campos, Marcelo, et al.
Published: (2025)

On the asymptotic behavior of online Ramsey numbers for stars, paths and cycles
by: Beilis, Sam, et al.
Published: (2026)

On the anti-Ramsey threshold
by: Kuperwasser, Eden
Published: (2025)

Ramsey numbers for 1-degenerate 3-graphs
by: Allen, Peter, et al.
Published: (2025)

On generalized Ramsey numbers in the non-integral regime
by: Bennett, Patrick, et al.
Published: (2022)

A New Lower Bound for the Diagonal Poset Ramsey Numbers
by: Ivan, Maria-Romina, et al.
Published: (2026)

Ramsey Number Counterexample Checking and One Vertex Extension Linearly Bound by $s$ and $t$
by: Lehavi, Adam M.
Published: (2024)

Ordered Ramsey and Turán numbers of alternating paths and their variants
by: Kucheriya, Gaurav, et al.
Published: (2026)

Off-diagonal Ramsey numbers for slowly growing hypergraphs
by: Mattheus, Sam, et al.
Published: (2024)

On the use of senders for asymmetric tuples of cliques in Ramsey theory
by: Boyadzhiyska, Simona, et al.
Published: (2022)

Polynomial-to-exponential transition in 3-uniform Ramsey numbers
by: Ascoli, Ruben, et al.
Published: (2025)

Ramsey simplicity of random graphs
by: Boyadzhiyska, Simona, et al.
Published: (2021)

Unavoidable subgraphs in Ramsey graphs
by: Reiher, Christian, et al.
Published: (2025)

The Ramsey number of the 4-cycle versus a book graph
by: Dou, Chunyang, et al.
Published: (2025)

Ramsey property for spaces with bilinear forms
by: Ivanov, Aleksander, et al.
Published: (2025)

Canonical theorems in geometric Ramsey theory
by: Gehér, Panna, et al.
Published: (2024)

Gaussian random graphs and Ramsey numbers
by: Hunter, Zach, et al.
Published: (2025)

Ramsey with purple edges
by: Lesgourgues, Thomas, et al.
Published: (2025)

Size-Ramsey numbers of graphs with maximum degree three
by: Draganić, Nemanja, et al.
Published: (2022)

T-Tetrominos in Arithmetic Progression
by: Feller, Emily, et al.
Published: (2022)

Max-norm Ramsey Theory
by: Frankl, Nóra, et al.
Published: (2021)

An exact value for the Ramsey number $R(K_5, K_{5-e})$
by: Angeltveit, Vigleik
Published: (2026)

Ramsey goodness of stars and fans for the Hajós graph
by: He, Jiafu, et al.
Published: (2025)

Disproofs of four Gallai-Ramsey-type conjectures
by: Zhang, Yanbo, et al.
Published: (2024)

When are off-diagonal hypergraph Ramsey numbers polynomial?
by: Conlon, David, et al.
Published: (2024)

All rectangles exhibit canonical Ramsey property
by: Ge, Gennian, et al.
Published: (2025)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// 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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