Three color Ramsey numbers for graphs with at most 4 vertices

For given graphs H1, H2, H3, the 3-color Ramsey number R(H1, H2, H3) is the smallest integer n such that if we arbitrarily color the edges of the complete graph of order n with 3 colors, then it always contains a monochromatic copy of Hi colored with i, for some 1 6 i 6 3. We study the bounds on 3-c...

ver descrição completa

Detalhes bibliográficos
Autores: Boza Prieto, Luis, Dybizbanski, J., Dzido, T.
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2012
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/163885
Acesso em linha:https://hdl.handle.net/11441/163885
https://doi.org/10.37236/2160
Access Level:acceso abierto
id ES_29ddbde0219bf04274c557dbd2e53aac
oai_identifier_str oai:idus.us.es:11441/163885
network_acronym_str ES
network_name_str España
repository_id_str
spelling Three color Ramsey numbers for graphs with at most 4 verticesBoza Prieto, LuisDybizbanski, J.Dzido, T.For given graphs H1, H2, H3, the 3-color Ramsey number R(H1, H2, H3) is the smallest integer n such that if we arbitrarily color the edges of the complete graph of order n with 3 colors, then it always contains a monochromatic copy of Hi colored with i, for some 1 6 i 6 3. We study the bounds on 3-color Ramsey numbers R(H1, H2, H3), where Hi is an isolate-free graph different from K2 with at most four vertices, establishing that R(P4, C4, K4) = 14, R(C4, K3, K4−e) = 17, R(C4, K3+e, K4−e) = 17, R(C4, K4− e, K4−e) = 19, 28 6 R(C4, K4−e, K4) 6 36, R(K3, K4−e, K4) 6 41, R(K4−e, K4− e, K4) 6 59 and R(K4−e, K4, K4) 6 113. Also, we prove that R(K3+e, K4−e, K4− e) = R(K3, K4 − e, K4 − e), R(C4, K3 + e, K4) 6 max{R(C4, K3, K4), 29} 6 32, R(K3 +e, K4 −e, K4) 6 max{R(K3, K4 −e, K4), 33} 6 41 and R(K3 +e, K4, K4) 6 max{R(K3, K4, K4), 2R(K3, K3, K4) + 2} 6 79.Electronic Journal of CombinatoricsMatemática Aplicada I2012info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/163885https://doi.org/10.37236/2160reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésElectronic Journal of Combinatorics, 19 (4).https://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i4p47info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1638852026-06-17T12:51:07Z
dc.title.none.fl_str_mv Three color Ramsey numbers for graphs with at most 4 vertices
title Three color Ramsey numbers for graphs with at most 4 vertices
spellingShingle Three color Ramsey numbers for graphs with at most 4 vertices
Boza Prieto, Luis
title_short Three color Ramsey numbers for graphs with at most 4 vertices
title_full Three color Ramsey numbers for graphs with at most 4 vertices
title_fullStr Three color Ramsey numbers for graphs with at most 4 vertices
title_full_unstemmed Three color Ramsey numbers for graphs with at most 4 vertices
title_sort Three color Ramsey numbers for graphs with at most 4 vertices
dc.creator.none.fl_str_mv Boza Prieto, Luis
Dybizbanski, J.
Dzido, T.
author Boza Prieto, Luis
author_facet Boza Prieto, Luis
Dybizbanski, J.
Dzido, T.
author_role author
author2 Dybizbanski, J.
Dzido, T.
author2_role author
author
dc.contributor.none.fl_str_mv Matemática Aplicada I
description For given graphs H1, H2, H3, the 3-color Ramsey number R(H1, H2, H3) is the smallest integer n such that if we arbitrarily color the edges of the complete graph of order n with 3 colors, then it always contains a monochromatic copy of Hi colored with i, for some 1 6 i 6 3. We study the bounds on 3-color Ramsey numbers R(H1, H2, H3), where Hi is an isolate-free graph different from K2 with at most four vertices, establishing that R(P4, C4, K4) = 14, R(C4, K3, K4−e) = 17, R(C4, K3+e, K4−e) = 17, R(C4, K4− e, K4−e) = 19, 28 6 R(C4, K4−e, K4) 6 36, R(K3, K4−e, K4) 6 41, R(K4−e, K4− e, K4) 6 59 and R(K4−e, K4, K4) 6 113. Also, we prove that R(K3+e, K4−e, K4− e) = R(K3, K4 − e, K4 − e), R(C4, K3 + e, K4) 6 max{R(C4, K3, K4), 29} 6 32, R(K3 +e, K4 −e, K4) 6 max{R(K3, K4 −e, K4), 33} 6 41 and R(K3 +e, K4, K4) 6 max{R(K3, K4, K4), 2R(K3, K3, K4) + 2} 6 79.
publishDate 2012
dc.date.none.fl_str_mv 2012
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/163885
https://doi.org/10.37236/2160
url https://hdl.handle.net/11441/163885
https://doi.org/10.37236/2160
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Electronic Journal of Combinatorics, 19 (4).
https://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i4p47
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Electronic Journal of Combinatorics
publisher.none.fl_str_mv Electronic Journal of Combinatorics
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869405034765090816
score 15,812429

Registos relacionados