Size-4 Counterexamples to the Sidon-Extension Conjecture

Fuente: arXiv

Saved in:

Bibliographic Details
Main Author:	Niu, Tong
Format:	Preprint
Published:	2026
Subjects:	Combinatorics Discrete Mathematics
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Toward Grünbaum's Conjecture
by: Ortlieb, Christian, et al.
Published: (2024)

The Non-Cancelling Intersections Conjecture
by: Amarilli, Antoine, et al.
Published: (2024)

On Tuza's Conjecture in Dense Graphs
by: Chahua, Luis, et al.
Published: (2024)

HIST-Critical Graphs and Malkevitch's Conjecture
by: Goedgebeur, Jan, et al.
Published: (2024)

On the Conjecture of the Representation Number of Bipartite Graphs
by: Mozhui, Khyodeno, et al.
Published: (2025)

Word-Representability of Split Graphs with Independent Set of Size 4
by: Roy, Suchanda, et al.
Published: (2025)

A Proof of Bala's General-$m$ Representation of the Harmonic Numbers
by: Niu, Tong
Published: (2026)

A Refutation of the Pach-Tardos Conjecture for 0-1 Matrices
by: Pettie, Seth, et al.
Published: (2024)

Analogues of Bermond-Bollobás Conjecture for Cages Yield Expander Families
by: Eze, Leonard Chidiebere, et al.
Published: (2024)

On the Extension Theorem for Packing Steiner Forests
by: Zeng, Jinghan A
Published: (2026)

Extension of the Gyárfás-Sumner conjecture to signed graphs
by: Aubian, Guillaume, et al.
Published: (2025)

From the Finite to the Infinite: Sharper Asymptotic Bounds on Norin's Conjecture via SAT
by: Kirchweger, Markus, et al.
Published: (2025)

A Proof of the 2004 Albert-Grossman-Nowakowski-Wolfe Conjecture on Alternating Linear Clobber
by: Chen, Xinyue, et al.
Published: (2025)

Linear Extensions of Rotor-Routing in Directed Graphs: Reachability Problems
by: Auger, David, et al.
Published: (2024)

Polytopes with Bounded Integral Slack Matrices Have Sub-Exponential Extension Complexity
by: Dong, Sally, et al.
Published: (2023)

Counterexamples to a Conjecture on Laplacian Ratios of Trees
by: Pant, Priyanshu
Published: (2026)

A Proof of Talagrand's Creating Large Sets Conjecture
by: Fang, Xuan, et al.
Published: (2025)

4-tangrams are 4-avoidable
by: Ochem, Pascal, et al.
Published: (2025)

Rainbow Arborescence Conjecture
by: Bérczi, Kristóf, et al.
Published: (2024)

The Dominating 4-Colour Theorem
by: Girão, António, et al.
Published: (2026)

($P_2+P_4$, $K_4-e$)-free graphs are nearly $ω$-colorable
by: Angeliya, C. U., et al.
Published: (2025)

Forcing quasirandomness with 4-point permutations
by: Kráľ, Daniel, et al.
Published: (2024)

Winding number and circular 4-coloring of signed graphs
by: Gujgiczer, Anna, et al.
Published: (2023)

The Graph Coloring Game on $4\times n$-Grids
by: Brosse, Caroline, et al.
Published: (2024)

Pushing Cops and Robber on Graphs of Maximum Degree 4
by: Gahlawat, Harmender
Published: (2025)

On the minimum number of arcs in $4$-dicritical oriented graphs
by: Havet, Frédéric, et al.
Published: (2023)

An Improved Bound for the Beck-Fiala Conjecture
by: Bansal, Nikhil, et al.
Published: (2025)

Separating the edges of a graph by cycles and by subdivisions of $K_4$
by: Botler, Fábio, et al.
Published: (2024)

A Simplified Proof for the Edge-Density of 4-Planar Graphs
by: Büngener, Aaron
Published: (2025)

2-distance 4-coloring of planar subcubic graphs with girth at least 21
by: La, Hoang, et al.
Published: (2021)

Smoothed Analysis of the Komlós Conjecture: Rademacher Noise
by: Aigner-Horev, Elad, et al.
Published: (2023)

Improved Upper Bound for the Size of a Trifferent Code
by: Bhandari, Siddharth, et al.
Published: (2024)

The 27-qubit Counterexample to the LU-LC Conjecture is Minimal
by: Claudet, Nathan
Published: (2026)

Computational Verification of the Buratti--Horak--Rosa Conjecture for Small Integers and Inductive Approaches
by: Naik, Ranjan N
Published: (2025)

Sizes of flat maximal antichains of subsets
by: Griggs, Jerrold R., et al.
Published: (2023)

Some Counterexamples for Compatible Triangulations
by: Barnson, Cody, et al.
Published: (2016)

A Brooks-type theorem for the k-choosability of graphs with maximum local edge-connectivity k
by: Bastida, Sam, et al.
Published: (2026)

Excluding an apex-forest or a fan as quickly as possible
by: Claus, Quentin, et al.
Published: (2026)

On Patterns and Languages in 1-11-Representations of Graphs
by: Das, Biswajit, et al.
Published: (2026)

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'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
language	"en"
VUFIND_SESSION	"c5f4bfc6673b8d1f8487bab30d1bb88f"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790883503.6302 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "c5f4bfc6673b8d1f8487bab30d1bb88f" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"language=en; VUFIND_SESSION=c5f4bfc6673b8d1f8487bab30d1bb88f; ui=standard"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"35403"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2604_25214/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2604_25214/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790883503.6263
REQUEST_TIME	1790883503

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
language	"en"
VUFIND_SESSION	"c5f4bfc6673b8d1f8487bab30d1bb88f"
ui	"standard"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790883503.6302 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "c5f4bfc6673b8d1f8487bab30d1bb88f" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"language=en; VUFIND_SESSION=c5f4bfc6673b8d1f8487bab30d1bb88f; ui=standard"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"35403"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2604_25214/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2604_25214/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790883503.6263
REQUEST_TIME	1790883503

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: