The conformable condition for Nanodiscs
Resumo
We investigate the total coloring of fullerene nanodiscs, a subclass of cubic planar graphs with girth 5 arising in Chemistry, motivated by a conjecture about the nonexistence of a Type 2 cubic graph of girth at least 5. We give a combinatorial description and then a conformable coloring for an infinite family of fullerene nanodiscs.
Palavras-chave:
Graph theory, Cubic graphs, Total Coloring, Conformable Coloring
Referências
Behzad, M. (1965). Graphs and their chromatic numbers. Michigan State University.
Brinkmann, G., Preissmann, M., and Sasaki, D. (2015). Snarks with total chromatic number 5. Discrete Mathematics and Theoretical Computer Science, 17:369–382.
Chetwynd, A. and Hilton, A. (1988). Some refinements of the total chromatic number conjecture. Congressus Numerantium, 66:195–216.
da Cruz, M., de Figueiredo, C., Sasaki, D., and Costa, M. (2021). Hunting a Type 2 fullerene nanodisc. Matemática Contemporânea, 48:126–136.
Kostochka, A. V. (1996). The total chromatic number of any multigraph with maximum degree five is at most seven. Discrete Mathematics, 162:199–214.
Nicodemos, D. (2017). Diâmetro de Grafos Fulerenes e Transversalidade de Ciclos Ímpares de Fuleróides-(3, 4, 5, 6). PhD thesis, Universidade Federal do Rio de Janeiro.
Sánchez-Arroyo, A. (1989). Determining the total colouring number is NP-hard. Discrete Mathematics, 78(3):315–319.
Vizing, V. (1964). On an estimate of the chromatic class of a p-graph. Discret Analiz, 3:25–30.
Brinkmann, G., Preissmann, M., and Sasaki, D. (2015). Snarks with total chromatic number 5. Discrete Mathematics and Theoretical Computer Science, 17:369–382.
Chetwynd, A. and Hilton, A. (1988). Some refinements of the total chromatic number conjecture. Congressus Numerantium, 66:195–216.
da Cruz, M., de Figueiredo, C., Sasaki, D., and Costa, M. (2021). Hunting a Type 2 fullerene nanodisc. Matemática Contemporânea, 48:126–136.
Kostochka, A. V. (1996). The total chromatic number of any multigraph with maximum degree five is at most seven. Discrete Mathematics, 162:199–214.
Nicodemos, D. (2017). Diâmetro de Grafos Fulerenes e Transversalidade de Ciclos Ímpares de Fuleróides-(3, 4, 5, 6). PhD thesis, Universidade Federal do Rio de Janeiro.
Sánchez-Arroyo, A. (1989). Determining the total colouring number is NP-hard. Discrete Mathematics, 78(3):315–319.
Vizing, V. (1964). On an estimate of the chromatic class of a p-graph. Discret Analiz, 3:25–30.
Publicado
31/07/2022
Como Citar
CRUZ, Mariana M. F. da; FIGUEIREDO, Celina M. H. de; SASAKI, Diana; COSTA, Marcus T..
The conformable condition for Nanodiscs. In: ENCONTRO DE TEORIA DA COMPUTAÇÃO (ETC), 7. , 2022, Niterói.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2022
.
p. 17-20.
ISSN 2595-6116.
DOI: https://doi.org/10.5753/etc.2022.222595.
