Coloração total equilibrada do snark Estrela Dupla
Resumo
Em 2016, Dantas et al. levantaram o questionamento se existe um grafo cúbico Tipo 1 com cintura pelo menos 5 e que possua número cromático total equilibrado 5, o que motivou este trabalho. Nós provamos que o snark Estrela Dupla possui número cromático total equilibrado 4 contribuindo para esta questão como uma evidência negativa.Referências
Araújo, R. and Sasaki, D. (2023). Coloraçao total equilibrada dos snarks de loupekine. In Anais do VIII Encontro de Teoria da Computação, pages 20–24. SBC.
Behzad, M. (1965). Graphs and Their Chromatic Numbers. PhD thesis, Michigan State University, Michigan.
Campos, C., Dantas, S., and de Mello, C. (2011). The total-chromatic number of some families of snarks. Discrete Math., 311:984–988.
Cavicchioli, A., Murgolo, T., Ruini, B., and Spaggiari, F. (2003). Special classes of snarks. Acta Applicandae Mathematica, 76:57–88.
Cordeiro, L., Dantas, S., and Sasaki, D. (2017). On equitable total colouring of loupekine snarks and their products. Mat. Cont., 45:77–85.
Dantas, S., de Figueiredo, C. M. H., Mazzuoccolo, G., Preissman, M., dos Santos, V. F., and Sasaki, D. (2016). On the equitable total chromatic number of cubic graphs. Discrete Appl. Math., 209:84–91.
Fu, H.-L. (1994). Some results on equalized total coloring. Congressus numerantium, pages 111–120.
Isaacs, R. (1975). Loupekhine’s snarks: A bi-family of non-tait-colorable graphs. Tec. Report.
Rosenfeld, M. (1971). On the total chromatic number of a graph. Israel J. Math, pages 396–402.
Sasaki, D., Dantas, S., de Figueiredo, C. M. H., Mazzuoccolo, G., and Preissman, M. (2014). The hunting of a snark with total chromatic number 5. Discrete Appl. Math., 164:470–481.
Tait, P. G. (1878-1880). Remarks on the colouring of maps. In Proceedings of the RSE, pages 501–503, 729, Edinburgh, Scotland.
Vizing, V. (1964). On an estimate of the chromatic class of a p-graph. Diskret. Analiz., pages 25–30.
Wang, W. (2002). Equitable total coloring of graphs with maximum degree 3. Graphs Comb, 18:677–685.
Behzad, M. (1965). Graphs and Their Chromatic Numbers. PhD thesis, Michigan State University, Michigan.
Campos, C., Dantas, S., and de Mello, C. (2011). The total-chromatic number of some families of snarks. Discrete Math., 311:984–988.
Cavicchioli, A., Murgolo, T., Ruini, B., and Spaggiari, F. (2003). Special classes of snarks. Acta Applicandae Mathematica, 76:57–88.
Cordeiro, L., Dantas, S., and Sasaki, D. (2017). On equitable total colouring of loupekine snarks and their products. Mat. Cont., 45:77–85.
Dantas, S., de Figueiredo, C. M. H., Mazzuoccolo, G., Preissman, M., dos Santos, V. F., and Sasaki, D. (2016). On the equitable total chromatic number of cubic graphs. Discrete Appl. Math., 209:84–91.
Fu, H.-L. (1994). Some results on equalized total coloring. Congressus numerantium, pages 111–120.
Isaacs, R. (1975). Loupekhine’s snarks: A bi-family of non-tait-colorable graphs. Tec. Report.
Rosenfeld, M. (1971). On the total chromatic number of a graph. Israel J. Math, pages 396–402.
Sasaki, D., Dantas, S., de Figueiredo, C. M. H., Mazzuoccolo, G., and Preissman, M. (2014). The hunting of a snark with total chromatic number 5. Discrete Appl. Math., 164:470–481.
Tait, P. G. (1878-1880). Remarks on the colouring of maps. In Proceedings of the RSE, pages 501–503, 729, Edinburgh, Scotland.
Vizing, V. (1964). On an estimate of the chromatic class of a p-graph. Diskret. Analiz., pages 25–30.
Wang, W. (2002). Equitable total coloring of graphs with maximum degree 3. Graphs Comb, 18:677–685.
Publicado
21/07/2024
Como Citar
ARAÚJO, Rieli; SASAKI, Diana.
Coloração total equilibrada do snark Estrela Dupla. In: ENCONTRO DE TEORIA DA COMPUTAÇÃO (ETC), 9. , 2024, Brasília/DF.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2024
.
p. 21-24.
ISSN 2595-6116.
DOI: https://doi.org/10.5753/etc.2024.2115.
