:: Library Catalog

Saved in:

Bibliographic Details
Main Authors:	Ma, Hui, Hao, Lili, Yang, Weihua
Format:	Preprint
Published:	2025
Subjects:	Combinatorics
Online Access:	https://arxiv.org/abs/2505.04189
Tags:	Add Tag No Tags, Be the first to tag this record!

Hamilton cycles in tough $(2P_2 \cup P_1)$-free graphs
by: Shan, Songling, et al.
Published: (2025)

On hamiltonian cycles of 1-tough $(P_{2} \cup kP_{1})$-free graphs
by: Sanka, Masahiro
Published: (2026)

2-factors in $\frac{3}{2}$-tough maximal planar graphs
by: Hao, Lili, et al.
Published: (2025)

A Fan-type condition for cycles in $1$-tough and $k$-connected $(P_2\cup kP_1)$-free graphs
by: Hu, Zhiquan, et al.
Published: (2024)

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

Every $2k$-connected $(P_2\cup kP_1)$-free graph with toughness greater than one is hamiltonian-connected
by: Liu, Feng
Published: (2025)

Perfect divisions in ($P_2 \cup P_4$, bull)-free graphs
by: Chen, Lizhong, et al.
Published: (2025)

Optimal chromatic bound for ($P_2\cup P_4$, HVN)-free graphs
by: Chen, Lizhong, et al.
Published: (2025)

Colouring ($P_2\cup P_4$, diamond)-free graphs with $ω$ colours
by: Wang, Hongyang
Published: (2025)

Perfect divisibility of (fork, antifork$\cup K_1$)-free graphs
by: Chen, Ran, et al.
Published: (2025)

Sufficient conditions for $t$-tough graphs to be Hamiltonian and pancyclic or bipartite
by: Liu, Xiangge, et al.
Published: (2025)

A spectral condition for Hamilton cycles in tough bipartite graphs
by: Ai, Lianyang, et al.
Published: (2025)

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

An optimal chromatic bound for ($P_2+P_3$, gem)-free graphs
by: Char, Arnab, et al.
Published: (2024)

Reconfiguration graph for vertex colorings for ($P_2$+$P_3$, $C_4$)-free graphs
by: Belavadi, M., et al.
Published: (2025)

Structure, Perfect Divisibility and Coloring of ($P_2\cup P_4, C_3$)-Free Graphs
by: Chen, Ran, et al.
Published: (2025)

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

Constructions of minimally $t$-tough regular graphs
by: Cheng, Kun, et al.
Published: (2024)

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)

Minimally tough series-parallel graphs with toughness at least $1/2$
by: Katona, Gyula Y., et al.
Published: (2025)

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

Degree sequence condition for Hamiltonicity in tough graphs
by: Shan, Songling, et al.
Published: (2024)

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

Balanced clique subdivisions and cycles lengths in $K_{s, t}$-free graphs
by: Hou, Jianfeng, et al.
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)

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

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

Powers of Hamiltonian cycles in randomly augmented Pósa-Seymour graphs
by: Antoniuk, Sylwia, et al.
Published: (2025)

Sufficient conditions for spanning $k$-trees in tough graphs
by: Jia, Caili, et al.
Published: (2026)

Minimal toughness in special graph classes
by: Katona, Gyula Y., et al.
Published: (2018)

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

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

Fractional factors and component factors in graphs with isolated toughness smaller than 1
by: Wolf, Isaak H.
Published: (2023)

Vertex-critical graphs in subfamilies of $(P_4+\ell P_1)$-free graphs
by: Beaton, Iain, et al.
Published: (2026)

On graphs without cycles of length 1 modulo 3
by: Bai, Yandong, et al.
Published: (2025)

On the existence of minimally tough graphs having large minimum degrees
by: Hasanvand, Morteza
Published: (2025)

Eigenvalues, edge-disjoint perfect matchings and toughness of regular graphs
by: Zhang, Wenqian
Published: (2024)

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

Minimum saturated graphs without $4$-cycles and $5$-cycles
by: Ma, Yue
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'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
VUFIND_SESSION	"374cc3d2cd138f9ebc381109d4233ae7"
ui	"standard"
language	"en"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1784430306.0357 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "374cc3d2cd138f9ebc381109d4233ae7" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1583}
SessionHelper	Laminas\Stdlib\ArrayObject {#1772}

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=374cc3d2cd138f9ebc381109d4233ae7; ui=standard; language=en"
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	"216.73.217.30"
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	"53284"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2505_04189/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2505_04189/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1784430306.0316
REQUEST_TIME	1784430306

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
VUFIND_SESSION	"374cc3d2cd138f9ebc381109d4233ae7"
ui	"standard"
language	"en"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1784430306.0357 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "374cc3d2cd138f9ebc381109d4233ae7" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1583}
SessionHelper	Laminas\Stdlib\ArrayObject {#1772}

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=374cc3d2cd138f9ebc381109d4233ae7; ui=standard; language=en"
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	"216.73.217.30"
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	"53284"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2505_04189/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2505_04189/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1784430306.0316
REQUEST_TIME	1784430306

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: