The chromatic number of $\mathbb{R}^8$ is at least 25

Fuente: arXiv

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Parts, Jaan
Format:	Preprint
Veröffentlicht:	2026
Schlagworte:	Combinatorics
Online-Zugang:	Acceder al recurso
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Ähnliche Einträge

The fractional chromatic number of the plane is at least 4
von: Matolcsi, Máté, et al.
Veröffentlicht: (2023)

Extremal triangle-free graphs with chromatic number at least four
von: Ren, Sijie, et al.
Veröffentlicht: (2024)

Spectral extremal results for triangle-free graphs with chromatic number at least four
von: Zhu, Yinfen, et al.
Veröffentlicht: (2026)

The chromatic number of the plane with an interval of forbidden distances is at least 7
von: Voronov, Vsevolod
Veröffentlicht: (2023)

Upper bounds on chromatic number of $\mathbb{E}^n$ in low dimensions
von: Arman, Andrii, et al.
Veröffentlicht: (2021)

Minimum non-chromatic-choosable graphs with given chromatic number
von: Zhu, Jialu, et al.
Veröffentlicht: (2022)

On graphs with maximum difference between game chromatic number and chromatic number
von: Hollom, Lawrence
Veröffentlicht: (2023)

On the chromatic numbers of Johnson type graphs
von: Cherkashin, Danila
Veröffentlicht: (2025)

The $d$-chromatic Ramsey number for stars
von: Yi, Aijun, et al.
Veröffentlicht: (2025)

Common graphs with arbitrary chromatic number
von: Kral, Daniel, et al.
Veröffentlicht: (2022)

On the chromatic number of powers of subdivisions of graphs
von: Anastos, Michael, et al.
Veröffentlicht: (2024)

Bounds for the Grundy chromatic number of graphs in terms of domination number
von: Khaleghi, Abbas, et al.
Veröffentlicht: (2022)

Quantum independence and chromatic numbers
von: Godsil, Chris, et al.
Veröffentlicht: (2024)

On the distinguishing chromatic number in hereditary graph classes
von: Brause, Christoph, et al.
Veröffentlicht: (2025)

Acyclic subgraphs of tournaments with high chromatic number
von: Fox, Jacob, et al.
Veröffentlicht: (2019)

A note on the maximum ratio between chromatic number and clique number
von: Araujo, Igor, et al.
Veröffentlicht: (2025)

The chromatic number of 4-dimensional lattices
von: Vallentin, Frank, et al.
Veröffentlicht: (2024)

The chromatic number of triangle-free hypergraphs
von: Li, Lina, et al.
Veröffentlicht: (2022)

Linear versus centred chromatic numbers
von: Bose, Prosenjit, et al.
Veröffentlicht: (2022)

On the chromatic numbers of 3-dimensional slices
von: Cherkashin, D. D., et al.
Veröffentlicht: (2022)

Circular chromatic number of Cartesian product of signed graphs
von: Desire, Ebode Atangana Pie
Veröffentlicht: (2024)

On Sierpiński packing chromatic number and recognition of Sierpiński products
von: Holub, Přemysl, et al.
Veröffentlicht: (2025)

Bounds for the independence and chromatic numbers of locally sparse graphs
von: Dhawan, Abhishek
Veröffentlicht: (2024)

Fractional balanced chromatic number of signed subcubic graphs
von: Hu, Xiaolan, et al.
Veröffentlicht: (2025)

On the Turán number of odd-ballooning of $3$-chromatic graphs
von: Fang, Longfei, et al.
Veröffentlicht: (2025)

Eigenvalue bounds for the quantum chromatic number of graph powers
von: Abiad, Aida, et al.
Veröffentlicht: (2025)

The oriented chromatic number of random graphs of bounded degree
von: Gunderson, Karen, et al.
Veröffentlicht: (2022)

On the quantum chromatic number of Hamming and generalized Hadamard graphs
von: Cao, Xiwang, et al.
Veröffentlicht: (2025)

Suns in triangle-free graphs of large chromatic number
von: Hajebi, Sepehr, et al.
Veröffentlicht: (2025)

The chromatic number of very dense random graphs
von: Yan, Zhifei
Veröffentlicht: (2024)

On the chromatic number of random triangle-free graphs
von: Mizgerd, Clayton, et al.
Veröffentlicht: (2025)

On the number of pairwise touching cylinders in $\mathbb{R}^d$
von: Solymosi, Jozsef, et al.
Veröffentlicht: (2025)

Fractional balanced chromatic number and arboricity of planar (signed) graphs
von: Naserasr, Reza, et al.
Veröffentlicht: (2025)

On graphs with chromatic number and maximum degree both equal to nine
von: Galindo, Rachel, et al.
Veröffentlicht: (2024)

Balanced-chromatic number and Hadwiger-like conjectures
von: Jiménez, Andrea, et al.
Veröffentlicht: (2023)

On cuts of small chromatic number in sparse graphs
von: Aubian, Guillaume, et al.
Veröffentlicht: (2025)

More results on the $z$-chromatic number of graphs
von: Khaleghi, Abbas, et al.
Veröffentlicht: (2023)

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

A note on a very abstract chromatic number and extremal problems
von: Gerbner, Dániel
Veröffentlicht: (2026)

A note on the chromatic number of the square of a sparse random graph
von: Frieze, Alan, et al.
Veröffentlicht: (2023)

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
VUFIND_SESSION	"8e9c674bfa6c224f50f0861b8975c5e8"
ui	"standard"
language	"de"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790882295.2451 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "8e9c674bfa6c224f50f0861b8975c5e8" ]`]
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	"VUFIND_SESSION=8e9c674bfa6c224f50f0861b8975c5e8; ui=standard; language=de"
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	"48802"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2603_14581/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2603_14581/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790882295.2405
REQUEST_TIME	1790882295

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler