Sobre coloração total dos grafos circulantes

Detalhes bibliográficos
Autor(a) principal: Alves Junior, Mauro Nigro
Data de Publicação: 2021
Outros Autores: mauronigro94@gmail.com
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Biblioteca Digital de Teses e Dissertações da UERJ
Texto Completo: http://www.bdtd.uerj.br/handle/1/21045
Resumo: A circulant graph Cn(d1, d2, • • • , dl) with 1 ≤ di ≤ bn 2 c, where di 6= dj , has vertex set V = {v0, v1, • • • , vn−1} and edge set E = Sl i=1 Ei , where Ei = {e i 0 , ei 1 , • • • , ei n−1} and e i j = vjvj+di , where the indexes of the vertices are considered modulo n. An edge of Ei is called edge of length di . A k-total coloring of a graph G is an assignment of k colors to the vertices and edges (elements) of G so that adjacent or incident elements have different colors. The total chromatic number of G is the smallest integer k for which G has a k-total coloring. The well known Total Coloring Conjecture states that the total chromatic number of a graph is either ∆(G) + 1 or ∆(G) + 2, where ∆(G) is the maximum degree of G. Graphs with χ 00(G) = ∆(G) + 1 are known as Type 1, and graphs with χ 00(G) = ∆(G) + 2 are known as Type 2. Some classical circulant graphs, such as the cycle graphs Cn ' Cn(1), the complete graphs Kn ' Cn(1, 2, ..., bn/2c), and the complete bipartite graphs Kn,n ' C2n(1, 3, 5, ..., k), where k is the biggest odd number such that k ≤ n, have their total chromatic number determined. Furthermore, the total chromatic number of every cubic circulant graph C2n(d, n) was determined by Hackmann and Kemnitz in 2004. There are many results in the well known powers of cycles graphs, an infinite family of circulant graphs Cn(1, 2, ..., k). In 2003, Campos and de Mello proved that Cn(1, 2) is Type 1, except for graph C7(1, 2) which is Type 2, and they conjectured that Cn(1, 2, ..., k), with 2 ≤ k ≤ bn/2c, is Type 2 if and only if n is odd and k < n/3 − 1. Recently, it was proved that this conjecture holds for k = 3 and k = 4. In 2008, Khennoufa and Togni proved that every 4-regular circulant graph C5p(1, k) is Type 1, for any positive integer p and k < 5p/2 with k ≡ 2 mod 5 or k ≡ 3 mod 5; and proved that C6p(1, k) is Type 1, for p ≥ 3 and k < 3p with k ≡ 1 mod 3 or k ≡ 2 mod 3. Furthermore, they vericated some particular cases with the help of the computer. In the same paper, Khennoufa and Togni conjectured that except for a finite number of Type 2, 4-regular circulant graphs are all Type 1. In this work, we studied all the results that envolved the state of art about total coloring of circulant graphs. Futhermore, we contribute to this conjecture by determining the total chromatic number of all graphs of the following three infinite families of 4-regular circulant graphs: Cn(2k, 3), k ≥ 1 and n = (8µ + 6λ)k, for non negative integers µ and λ; C3n(1, 3), for n > 1; and C3λp(1, p), λ ≥ 1 and p ≡ 0 mod 3, suggesting that the conjecture has a positive answer.
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spelling Nobrega, Diana Sasakihttp://lattes.cnpq.br/3041110572471417Pará, Telma Silveirahttp://lattes.cnpq.br/8994079152391652Faria, Luérbiohttp://lattes.cnpq.br/3965328361563422Sucupira, Rubens Andréhttp://lattes.cnpq.br/3720701359530948http://lattes.cnpq.br/7725025449551730Alves Junior, Mauro Nigromauronigro94@gmail.com2024-02-07T18:42:28Z2021-02-19Alves Junior, Mauro Nigro. Sobre coloração total dos grafos circulantes. 2021. 92f. Dissertação (Mestrado em Ciências Computacionais) - Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, 2021.http://www.bdtd.uerj.br/handle/1/21045A circulant graph Cn(d1, d2, • • • , dl) with 1 ≤ di ≤ bn 2 c, where di 6= dj , has vertex set V = {v0, v1, • • • , vn−1} and edge set E = Sl i=1 Ei , where Ei = {e i 0 , ei 1 , • • • , ei n−1} and e i j = vjvj+di , where the indexes of the vertices are considered modulo n. An edge of Ei is called edge of length di . A k-total coloring of a graph G is an assignment of k colors to the vertices and edges (elements) of G so that adjacent or incident elements have different colors. The total chromatic number of G is the smallest integer k for which G has a k-total coloring. The well known Total Coloring Conjecture states that the total chromatic number of a graph is either ∆(G) + 1 or ∆(G) + 2, where ∆(G) is the maximum degree of G. Graphs with χ 00(G) = ∆(G) + 1 are known as Type 1, and graphs with χ 00(G) = ∆(G) + 2 are known as Type 2. Some classical circulant graphs, such as the cycle graphs Cn ' Cn(1), the complete graphs Kn ' Cn(1, 2, ..., bn/2c), and the complete bipartite graphs Kn,n ' C2n(1, 3, 5, ..., k), where k is the biggest odd number such that k ≤ n, have their total chromatic number determined. Furthermore, the total chromatic number of every cubic circulant graph C2n(d, n) was determined by Hackmann and Kemnitz in 2004. There are many results in the well known powers of cycles graphs, an infinite family of circulant graphs Cn(1, 2, ..., k). In 2003, Campos and de Mello proved that Cn(1, 2) is Type 1, except for graph C7(1, 2) which is Type 2, and they conjectured that Cn(1, 2, ..., k), with 2 ≤ k ≤ bn/2c, is Type 2 if and only if n is odd and k < n/3 − 1. Recently, it was proved that this conjecture holds for k = 3 and k = 4. In 2008, Khennoufa and Togni proved that every 4-regular circulant graph C5p(1, k) is Type 1, for any positive integer p and k < 5p/2 with k ≡ 2 mod 5 or k ≡ 3 mod 5; and proved that C6p(1, k) is Type 1, for p ≥ 3 and k < 3p with k ≡ 1 mod 3 or k ≡ 2 mod 3. Furthermore, they vericated some particular cases with the help of the computer. In the same paper, Khennoufa and Togni conjectured that except for a finite number of Type 2, 4-regular circulant graphs are all Type 1. In this work, we studied all the results that envolved the state of art about total coloring of circulant graphs. Futhermore, we contribute to this conjecture by determining the total chromatic number of all graphs of the following three infinite families of 4-regular circulant graphs: Cn(2k, 3), k ≥ 1 and n = (8µ + 6λ)k, for non negative integers µ and λ; C3n(1, 3), for n > 1; and C3λp(1, p), λ ≥ 1 and p ≡ 0 mod 3, suggesting that the conjecture has a positive answer.Um grafo circulante Cn(d1, d2, • • • , dl) com 1 ≤ di ≤ bn 2 c, e di 6= dj , tem um conjunto de vértices V = {v0, v1, • • • , vn−1} e um conjunto de arestas E = Sl i=1 Ei , em que Ei = {e i 0 , ei 1 , • • • , ei n−1} e e i j = vjvj+di , sendo os índices dos vértices considerados em módulo n. Uma aresta de Ei é chamada de aresta de distância di . Uma k−coloração total de um grafo G é uma atribuição de k cores aos vértices e arestas de G tal que elementos adjacentes ou incidentes têm cor diferente. O número cromático total de G é o menor número inteiro k que G tem uma k−coloração total, denotado por χ 00(G). A Conjectura da Coloração Total afirma que o número cromático total ou é ∆(G)+1 ou é ∆(G)+2, onde ∆(G) é o grau máximo de G. Grafos com χ 00(G) = ∆(G) + 1 são chamados de Tipo 1 e grafos com χ 00(G) = ∆(G) + 2 são chamados de Tipo 2. Alguns grafos circulantes clássicos, como os grafos ciclos Cn ' Cn(1), os grafos completos Kn ' Cn(1, 2, ..., bn/2c) e os grafos bipartidos completos Kn,n ' C2n(1, 3, 5, ..., k) em que k é o maior número ímpar tal que k ≤ n, têm seus números cromáticos totais determinados. Além disso, os números cromáticos totais de todos os grafos circulantes cúbicos C2n(d, n) foram determinados por Hackmann e Kemnitz em 2004. Existem vários resultados conhecidos sobre as potências de ciclo, uma família infinita de grafos circulantes Cn(1, 2, ..., k). Em 2003, Campos provou que Cn(1, 2) é Tipo 1, exceto C7(1, 2) que é Tipo 2 e conjecturou que Cn(1, 2, ..., k) com 2 ≤ k ≤ bn/2c é Tipo 2, se e somente se, n é ímpar e k > n/3 − 1. Recentemente esta conjectura foi provada para k = 3 e k = 4. Em 2008, Khennoufa e Togni provaram que todo grafo circulante 4−regular C5p(1, k) é Tipo 1, para qualquer inteiro positivo p e k < 5p/2 com k ≡ 2 mod 5 e k ≡ 3 mod 5; e provaram que C6p(1, k) é Tipo 1, para p ≥ 3 e k < 3p com k ≡ 1 mod 3 ou k ≡ 2 mod 3. Além disso, eles verificaram casos particulares com o auxílio de um computador. Neste mesmo artigo, Khennoufa e Togni conjecturaram que exceto por uma coleção finita de Tipo 2, os grafos circulantes 4−regulares Cn(1, k) são Tipo 1. Neste trabalho, nós estudamos todos os resultados que abrangem o estado da arte sobre coloração total de grafos circulantes. E por fim, contribuímos para esta conjectura, determinando o número cromático total de todos os grafos das três seguintes famílias infinitas de circulantes 4−regulares: Cn(2k, 3), k ≥ 1 e n = (8µ + 6λ)k, para inteiros não negativos µ e λ; C3n(1, 3), para n > 1; e C3λp(1, p), λ ≥ 1 e p ≡ 0 mod 3, sugerindo que a conjectura é verdadeira.Submitted by Patrícia CTC/A (patbme@yahoo.com.br) on 2024-02-07T18:42:28Z No. of bitstreams: 1 Dissertação - Mauro Nigro Alves Junior - 2021 - Completa.pdf: 18511492 bytes, checksum: eeb2ee33b640a41bdd40040017b3a15a (MD5)Made available in DSpace on 2024-02-07T18:42:28Z (GMT). No. of bitstreams: 1 Dissertação - Mauro Nigro Alves Junior - 2021 - Completa.pdf: 18511492 bytes, checksum: eeb2ee33b640a41bdd40040017b3a15a (MD5) Previous issue date: 2021-02-19Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESapplication/pdfporUniversidade do Estado do Rio de JaneiroPrograma de Pós-Graduação em Ciências ComputacionaisUERJBrasilCentro de Tecnologia e Ciências::Instituto de Matemática e EstatísticaGraph theoryTotal coloringCirculant graphsTeoria dos grafosColoração totalGrafos circulantesCIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAOSobre coloração total dos grafos circulantesAbout total coloring of circulant graphsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccessreponame:Biblioteca Digital de Teses e Dissertações da UERJinstname:Universidade do Estado do Rio de Janeiro (UERJ)instacron:UERJORIGINALDissertação - Mauro Nigro Alves Junior - 2021 - Completa.pdfDissertação - Mauro Nigro Alves Junior - 2021 - Completa.pdfapplication/pdf18511492http://www.bdtd.uerj.br/bitstream/1/21045/2/Disserta%C3%A7%C3%A3o+-+Mauro+Nigro+Alves+Junior+-+2021+-+Completa.pdfeeb2ee33b640a41bdd40040017b3a15aMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-82011http://www.bdtd.uerj.br/bitstream/1/21045/1/license.txtba23dde015e31ff1802d858071d990cdMD511/210452024-02-27 14:34:50.686oai:www.bdtd.uerj.br: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Biblioteca Digital de Teses e Dissertaçõeshttp://www.bdtd.uerj.br/PUBhttps://www.bdtd.uerj.br:8443/oai/requestbdtd.suporte@uerj.bropendoar:29032024-02-27T17:34:50Biblioteca Digital de Teses e Dissertações da UERJ - Universidade do Estado do Rio de Janeiro (UERJ)false
dc.title.por.fl_str_mv Sobre coloração total dos grafos circulantes
dc.title.alternative.eng.fl_str_mv About total coloring of circulant graphs
title Sobre coloração total dos grafos circulantes
spellingShingle Sobre coloração total dos grafos circulantes
Alves Junior, Mauro Nigro
Graph theory
Total coloring
Circulant graphs
Teoria dos grafos
Coloração total
Grafos circulantes
CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAO
title_short Sobre coloração total dos grafos circulantes
title_full Sobre coloração total dos grafos circulantes
title_fullStr Sobre coloração total dos grafos circulantes
title_full_unstemmed Sobre coloração total dos grafos circulantes
title_sort Sobre coloração total dos grafos circulantes
author Alves Junior, Mauro Nigro
author_facet Alves Junior, Mauro Nigro
mauronigro94@gmail.com
author_role author
author2 mauronigro94@gmail.com
author2_role author
dc.contributor.advisor1.fl_str_mv Nobrega, Diana Sasaki
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/3041110572471417
dc.contributor.referee1.fl_str_mv Pará, Telma Silveira
dc.contributor.referee1Lattes.fl_str_mv http://lattes.cnpq.br/8994079152391652
dc.contributor.referee2.fl_str_mv Faria, Luérbio
dc.contributor.referee2Lattes.fl_str_mv http://lattes.cnpq.br/3965328361563422
dc.contributor.referee3.fl_str_mv Sucupira, Rubens André
dc.contributor.referee3Lattes.fl_str_mv http://lattes.cnpq.br/3720701359530948
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/7725025449551730
dc.contributor.author.fl_str_mv Alves Junior, Mauro Nigro
mauronigro94@gmail.com
contributor_str_mv Nobrega, Diana Sasaki
Pará, Telma Silveira
Faria, Luérbio
Sucupira, Rubens André
dc.subject.eng.fl_str_mv Graph theory
Total coloring
Circulant graphs
topic Graph theory
Total coloring
Circulant graphs
Teoria dos grafos
Coloração total
Grafos circulantes
CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAO
dc.subject.por.fl_str_mv Teoria dos grafos
Coloração total
Grafos circulantes
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::CIENCIA DA COMPUTACAO::MATEMATICA DA COMPUTACAO
description A circulant graph Cn(d1, d2, • • • , dl) with 1 ≤ di ≤ bn 2 c, where di 6= dj , has vertex set V = {v0, v1, • • • , vn−1} and edge set E = Sl i=1 Ei , where Ei = {e i 0 , ei 1 , • • • , ei n−1} and e i j = vjvj+di , where the indexes of the vertices are considered modulo n. An edge of Ei is called edge of length di . A k-total coloring of a graph G is an assignment of k colors to the vertices and edges (elements) of G so that adjacent or incident elements have different colors. The total chromatic number of G is the smallest integer k for which G has a k-total coloring. The well known Total Coloring Conjecture states that the total chromatic number of a graph is either ∆(G) + 1 or ∆(G) + 2, where ∆(G) is the maximum degree of G. Graphs with χ 00(G) = ∆(G) + 1 are known as Type 1, and graphs with χ 00(G) = ∆(G) + 2 are known as Type 2. Some classical circulant graphs, such as the cycle graphs Cn ' Cn(1), the complete graphs Kn ' Cn(1, 2, ..., bn/2c), and the complete bipartite graphs Kn,n ' C2n(1, 3, 5, ..., k), where k is the biggest odd number such that k ≤ n, have their total chromatic number determined. Furthermore, the total chromatic number of every cubic circulant graph C2n(d, n) was determined by Hackmann and Kemnitz in 2004. There are many results in the well known powers of cycles graphs, an infinite family of circulant graphs Cn(1, 2, ..., k). In 2003, Campos and de Mello proved that Cn(1, 2) is Type 1, except for graph C7(1, 2) which is Type 2, and they conjectured that Cn(1, 2, ..., k), with 2 ≤ k ≤ bn/2c, is Type 2 if and only if n is odd and k < n/3 − 1. Recently, it was proved that this conjecture holds for k = 3 and k = 4. In 2008, Khennoufa and Togni proved that every 4-regular circulant graph C5p(1, k) is Type 1, for any positive integer p and k < 5p/2 with k ≡ 2 mod 5 or k ≡ 3 mod 5; and proved that C6p(1, k) is Type 1, for p ≥ 3 and k < 3p with k ≡ 1 mod 3 or k ≡ 2 mod 3. Furthermore, they vericated some particular cases with the help of the computer. In the same paper, Khennoufa and Togni conjectured that except for a finite number of Type 2, 4-regular circulant graphs are all Type 1. In this work, we studied all the results that envolved the state of art about total coloring of circulant graphs. Futhermore, we contribute to this conjecture by determining the total chromatic number of all graphs of the following three infinite families of 4-regular circulant graphs: Cn(2k, 3), k ≥ 1 and n = (8µ + 6λ)k, for non negative integers µ and λ; C3n(1, 3), for n > 1; and C3λp(1, p), λ ≥ 1 and p ≡ 0 mod 3, suggesting that the conjecture has a positive answer.
publishDate 2021
dc.date.issued.fl_str_mv 2021-02-19
dc.date.accessioned.fl_str_mv 2024-02-07T18:42:28Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
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dc.identifier.citation.fl_str_mv Alves Junior, Mauro Nigro. Sobre coloração total dos grafos circulantes. 2021. 92f. Dissertação (Mestrado em Ciências Computacionais) - Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, 2021.
dc.identifier.uri.fl_str_mv http://www.bdtd.uerj.br/handle/1/21045
identifier_str_mv Alves Junior, Mauro Nigro. Sobre coloração total dos grafos circulantes. 2021. 92f. Dissertação (Mestrado em Ciências Computacionais) - Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, 2021.
url http://www.bdtd.uerj.br/handle/1/21045
dc.language.iso.fl_str_mv por
language por
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade do Estado do Rio de Janeiro
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Ciências Computacionais
dc.publisher.initials.fl_str_mv UERJ
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Centro de Tecnologia e Ciências::Instituto de Matemática e Estatística
publisher.none.fl_str_mv Universidade do Estado do Rio de Janeiro
dc.source.none.fl_str_mv reponame:Biblioteca Digital de Teses e Dissertações da UERJ
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repository.name.fl_str_mv Biblioteca Digital de Teses e Dissertações da UERJ - Universidade do Estado do Rio de Janeiro (UERJ)
repository.mail.fl_str_mv bdtd.suporte@uerj.br
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