Gallai-Ramsey Multiplicity for Rainbow Small Trees
Let G , H be two non-empty graphs and k be a positive integer. The Gallai-Ramsey number gr k ( G : H ) is defined as the minimum positive integer N such that for all n ≥ N , every k -edge-coloring of K n contains either a rainbow subgraph G or a monochromatic subgraph H . The Gallai-Ramsey multipli...
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creator | Li, Xueliang Si, Yuan |
description | Let
G
,
H
be two non-empty graphs and
k
be a positive integer. The Gallai-Ramsey number
gr
k
(
G
:
H
)
is defined as the minimum positive integer
N
such that for all
n
≥
N
, every
k
-edge-coloring of
K
n
contains either a rainbow subgraph
G
or a monochromatic subgraph
H
. The Gallai-Ramsey multiplicity
GM
k
(
G
:
H
)
is defined as the minimum total number of rainbow subgraphs
G
and monochromatic subgraphs
H
for all
k
-edge-colored
K
gr
k
(
G
:
H
)
. In this paper, we get some exact values of the Gallai-Ramsey multiplicity for rainbow small trees versus general monochromatic graphs under a sufficiently large number of colors. We also study the bipartite Gallai-Ramsey multiplicity. |
doi_str_mv | 10.1007/s00373-024-02819-z |
format | Article |
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G
,
H
be two non-empty graphs and
k
be a positive integer. The Gallai-Ramsey number
gr
k
(
G
:
H
)
is defined as the minimum positive integer
N
such that for all
n
≥
N
, every
k
-edge-coloring of
K
n
contains either a rainbow subgraph
G
or a monochromatic subgraph
H
. The Gallai-Ramsey multiplicity
GM
k
(
G
:
H
)
is defined as the minimum total number of rainbow subgraphs
G
and monochromatic subgraphs
H
for all
k
-edge-colored
K
gr
k
(
G
:
H
)
. In this paper, we get some exact values of the Gallai-Ramsey multiplicity for rainbow small trees versus general monochromatic graphs under a sufficiently large number of colors. We also study the bipartite Gallai-Ramsey multiplicity.</description><identifier>ISSN: 0911-0119</identifier><identifier>EISSN: 1435-5914</identifier><identifier>DOI: 10.1007/s00373-024-02819-z</identifier><language>eng</language><publisher>Tokyo: Springer Japan</publisher><subject>Combinatorics ; Engineering Design ; Graph coloring ; Graph theory ; Graphs ; Integers ; Mathematics ; Mathematics and Statistics ; Original Paper ; Trees (mathematics)</subject><ispartof>Graphs and combinatorics, 2024-08, Vol.40 (4), Article 91</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Japan KK 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-751eded29fb80b8e69b678d1b88e6abd30a6f73ace52fd511b79096aae8f72433</cites><orcidid>0000-0001-5905-0510</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00373-024-02819-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00373-024-02819-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27926,27927,41490,42559,51321</link.rule.ids></links><search><creatorcontrib>Li, Xueliang</creatorcontrib><creatorcontrib>Si, Yuan</creatorcontrib><title>Gallai-Ramsey Multiplicity for Rainbow Small Trees</title><title>Graphs and combinatorics</title><addtitle>Graphs and Combinatorics</addtitle><description>Let
G
,
H
be two non-empty graphs and
k
be a positive integer. The Gallai-Ramsey number
gr
k
(
G
:
H
)
is defined as the minimum positive integer
N
such that for all
n
≥
N
, every
k
-edge-coloring of
K
n
contains either a rainbow subgraph
G
or a monochromatic subgraph
H
. The Gallai-Ramsey multiplicity
GM
k
(
G
:
H
)
is defined as the minimum total number of rainbow subgraphs
G
and monochromatic subgraphs
H
for all
k
-edge-colored
K
gr
k
(
G
:
H
)
. In this paper, we get some exact values of the Gallai-Ramsey multiplicity for rainbow small trees versus general monochromatic graphs under a sufficiently large number of colors. We also study the bipartite Gallai-Ramsey multiplicity.</description><subject>Combinatorics</subject><subject>Engineering Design</subject><subject>Graph coloring</subject><subject>Graph theory</subject><subject>Graphs</subject><subject>Integers</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Original Paper</subject><subject>Trees (mathematics)</subject><issn>0911-0119</issn><issn>1435-5914</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kMFKAzEQhoMoWKsv4GnBc3Qm2d0kRynaChWh1nNIdhPZsu3WZItsn97oCt48DDOH7_8HPkKuEW4RQNxFAC44BZankajo8YRMMOcFLRTmp2QCCpECojonFzFuAKDAHCaEzU3bmoauzDa6IXs-tH2zb5uq6YfMdyFbmWZnu8_sdZu4bB2ci5fkzJs2uqvfPSVvjw_r2YIuX-ZPs_slrRhAT0WBrnY1U95KsNKVypZC1mhluo2tOZjSC24qVzBfF4hWKFClMU56wXLOp-Rm7N2H7uPgYq833SHs0kvNQZZSiZKrRLGRqkIXY3Be70OzNWHQCPrbjR7d6ORG_7jRxxTiYygmePfuwl_1P6kvYzVm2w</recordid><startdate>20240801</startdate><enddate>20240801</enddate><creator>Li, Xueliang</creator><creator>Si, Yuan</creator><general>Springer Japan</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-5905-0510</orcidid></search><sort><creationdate>20240801</creationdate><title>Gallai-Ramsey Multiplicity for Rainbow Small Trees</title><author>Li, Xueliang ; Si, Yuan</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-751eded29fb80b8e69b678d1b88e6abd30a6f73ace52fd511b79096aae8f72433</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Combinatorics</topic><topic>Engineering Design</topic><topic>Graph coloring</topic><topic>Graph theory</topic><topic>Graphs</topic><topic>Integers</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Original Paper</topic><topic>Trees (mathematics)</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Xueliang</creatorcontrib><creatorcontrib>Si, Yuan</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Graphs and combinatorics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Xueliang</au><au>Si, Yuan</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Gallai-Ramsey Multiplicity for Rainbow Small Trees</atitle><jtitle>Graphs and combinatorics</jtitle><stitle>Graphs and Combinatorics</stitle><date>2024-08-01</date><risdate>2024</risdate><volume>40</volume><issue>4</issue><artnum>91</artnum><issn>0911-0119</issn><eissn>1435-5914</eissn><abstract>Let
G
,
H
be two non-empty graphs and
k
be a positive integer. The Gallai-Ramsey number
gr
k
(
G
:
H
)
is defined as the minimum positive integer
N
such that for all
n
≥
N
, every
k
-edge-coloring of
K
n
contains either a rainbow subgraph
G
or a monochromatic subgraph
H
. The Gallai-Ramsey multiplicity
GM
k
(
G
:
H
)
is defined as the minimum total number of rainbow subgraphs
G
and monochromatic subgraphs
H
for all
k
-edge-colored
K
gr
k
(
G
:
H
)
. In this paper, we get some exact values of the Gallai-Ramsey multiplicity for rainbow small trees versus general monochromatic graphs under a sufficiently large number of colors. We also study the bipartite Gallai-Ramsey multiplicity.</abstract><cop>Tokyo</cop><pub>Springer Japan</pub><doi>10.1007/s00373-024-02819-z</doi><orcidid>https://orcid.org/0000-0001-5905-0510</orcidid></addata></record> |
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language | eng |
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source | SpringerNature Journals |
subjects | Combinatorics Engineering Design Graph coloring Graph theory Graphs Integers Mathematics Mathematics and Statistics Original Paper Trees (mathematics) |
title | Gallai-Ramsey Multiplicity for Rainbow Small Trees |
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