Chromatic number is Ramsey distinguishing
A graph G is Ramsey for a graph H if every colouring of the edges of G in two colours contains a monochromatic copy of H. Two graphs H 1 and H 2 are Ramsey equivalent if any graph G is Ramsey for H 1 if and only if it is Ramsey for H 2. A graph parameter s is Ramsey distinguishing if s ( H 1 ) ≠ s (...
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| Veröffentlicht in: | Journal of graph theory 2022-01, Vol.99 (1), p.152-161 |
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| container_title | Journal of graph theory |
| container_volume | 99 |
| creator | Savery, Michael |
| description | A graph
G is Ramsey for a graph
H if every colouring of the edges of
G in two colours contains a monochromatic copy of
H. Two graphs
H
1 and
H
2 are Ramsey equivalent if any graph
G is Ramsey for
H
1 if and only if it is Ramsey for
H
2. A graph parameter
s is Ramsey distinguishing if
s
(
H
1
)
≠
s
(
H
2
) implies that
H
1 and
H
2 are not Ramsey equivalent. In this paper we show that the chromatic number is a Ramsey distinguishing parameter. We also extend this to the multicolour case and use a similar idea to find another graph parameter which is Ramsey distinguishing. |
| doi_str_mv | 10.1002/jgt.22731 |
| format | Article |
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G is Ramsey for a graph
H if every colouring of the edges of
G in two colours contains a monochromatic copy of
H. Two graphs
H
1 and
H
2 are Ramsey equivalent if any graph
G is Ramsey for
H
1 if and only if it is Ramsey for
H
2. A graph parameter
s is Ramsey distinguishing if
s
(
H
1
)
≠
s
(
H
2
) implies that
H
1 and
H
2 are not Ramsey equivalent. In this paper we show that the chromatic number is a Ramsey distinguishing parameter. We also extend this to the multicolour case and use a similar idea to find another graph parameter which is Ramsey distinguishing.</description><identifier>ISSN: 0364-9024</identifier><identifier>EISSN: 1097-0118</identifier><identifier>DOI: 10.1002/jgt.22731</identifier><language>eng</language><publisher>Hoboken: Wiley Subscription Services, Inc</publisher><subject>chromatic number ; Coloring ; Equivalence ; Graph theory ; Parameters ; Ramsey distinguishing ; Ramsey equivalence</subject><ispartof>Journal of graph theory, 2022-01, Vol.99 (1), p.152-161</ispartof><rights>2021 Wiley Periodicals LLC</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2971-add8d90b0a73f534072bbbf92b85783f70f04a2c49f8a6bbba18380671378f593</citedby><cites>FETCH-LOGICAL-c2971-add8d90b0a73f534072bbbf92b85783f70f04a2c49f8a6bbba18380671378f593</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fjgt.22731$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fjgt.22731$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,776,780,1411,27901,27902,45550,45551</link.rule.ids></links><search><creatorcontrib>Savery, Michael</creatorcontrib><title>Chromatic number is Ramsey distinguishing</title><title>Journal of graph theory</title><description>A graph
G is Ramsey for a graph
H if every colouring of the edges of
G in two colours contains a monochromatic copy of
H. Two graphs
H
1 and
H
2 are Ramsey equivalent if any graph
G is Ramsey for
H
1 if and only if it is Ramsey for
H
2. A graph parameter
s is Ramsey distinguishing if
s
(
H
1
)
≠
s
(
H
2
) implies that
H
1 and
H
2 are not Ramsey equivalent. In this paper we show that the chromatic number is a Ramsey distinguishing parameter. We also extend this to the multicolour case and use a similar idea to find another graph parameter which is Ramsey distinguishing.</description><subject>chromatic number</subject><subject>Coloring</subject><subject>Equivalence</subject><subject>Graph theory</subject><subject>Parameters</subject><subject>Ramsey distinguishing</subject><subject>Ramsey equivalence</subject><issn>0364-9024</issn><issn>1097-0118</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><recordid>eNp1kEFLwzAUx4MoWKcHv0HB0w7dXpK2SY5SdCoDQeY5JG2zpaztTFqk337RevX0h_d-__fgh9A9hhUGIOtmP6wIYRRfoAiDYAlgzC9RBDRPEwEkvUY33jcQxhnwCC2Lg-tbNdgy7sZW1y62Pv5Qra-nuLJ-sN1-tP4Q4hZdGXX09d1fLtDn89OueEm275vX4nGblEQwnKiq4pUADYpRk9EUGNFaG0E0zxinhoGBVJEyFYarPKwU5pRDzjBl3GSCLtDDfPfk-q-x9oNs-tF14aUkmRBAMRUsUMuZKl3vvauNPDnbKjdJDPLHhAwm5K-JwK5n9tse6-l_UL5tdnPjDOEnXd8</recordid><startdate>202201</startdate><enddate>202201</enddate><creator>Savery, Michael</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>202201</creationdate><title>Chromatic number is Ramsey distinguishing</title><author>Savery, Michael</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2971-add8d90b0a73f534072bbbf92b85783f70f04a2c49f8a6bbba18380671378f593</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>chromatic number</topic><topic>Coloring</topic><topic>Equivalence</topic><topic>Graph theory</topic><topic>Parameters</topic><topic>Ramsey distinguishing</topic><topic>Ramsey equivalence</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Savery, Michael</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of graph theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Savery, Michael</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Chromatic number is Ramsey distinguishing</atitle><jtitle>Journal of graph theory</jtitle><date>2022-01</date><risdate>2022</risdate><volume>99</volume><issue>1</issue><spage>152</spage><epage>161</epage><pages>152-161</pages><issn>0364-9024</issn><eissn>1097-0118</eissn><abstract>A graph
G is Ramsey for a graph
H if every colouring of the edges of
G in two colours contains a monochromatic copy of
H. Two graphs
H
1 and
H
2 are Ramsey equivalent if any graph
G is Ramsey for
H
1 if and only if it is Ramsey for
H
2. A graph parameter
s is Ramsey distinguishing if
s
(
H
1
)
≠
s
(
H
2
) implies that
H
1 and
H
2 are not Ramsey equivalent. In this paper we show that the chromatic number is a Ramsey distinguishing parameter. We also extend this to the multicolour case and use a similar idea to find another graph parameter which is Ramsey distinguishing.</abstract><cop>Hoboken</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/jgt.22731</doi><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0364-9024 |
| ispartof | Journal of graph theory, 2022-01, Vol.99 (1), p.152-161 |
| issn | 0364-9024 1097-0118 |
| language | eng |
| recordid | cdi_proquest_journals_2599031397 |
| source | Wiley Online Library Journals Frontfile Complete |
| subjects | chromatic number Coloring Equivalence Graph theory Parameters Ramsey distinguishing Ramsey equivalence |
| title | Chromatic number is Ramsey distinguishing |
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