K-SUN PERTENECE A B2-EPG-HELLY

Autores/as

DOI:

https://doi.org/10.20873/uft.2447-4266.2023v9n1a25pt

Palabras clave:

B2-EPG, Graph Theory, Intersection Graphs, Helly Property, k-sun Graphs

Resumen

En este artículo exploramos la clase -EPG y la propiedad Helly. Presentamos resultados genéricos sobre las representaciones EPG y definimos términos que respaldan los otros resultados, además, finalizamos la investigación con un algoritmo original que construye una representación -EPG -Helly de cualquier grafo k-sun.

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Biografía del autor/a

Tanilson Dias dos Santos, Universidade Federal do Tocantins

Doutor em Engenharia de Sistemas e Computação - PESC/COPPE-UFRJ. Professor do Curso de Ciência da Computação - Universidade Federal do Tocantins. tanilson.dias@mail.uft.edu.br

Kedson Alves Silva, Universidade Federal do Tocantins

Bacharel em Ciência da Computação – Universidade Federal do Tocantins. alves.kedson@mail.uft.edu.br

Luiz Fernando dos Santos Marinho, Universidade Estadual do Tocantins

Bacharel em Ciência da Computação – Universidade Federal do Tocantins. fernando.marinho@mail.uft.edu.br

Citas

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ALCÓN, L.; MAZZOLENI, M. P.; SANTOS, T. D. Relationship among B1-EPG, VPT and EPT graphs classes. Discussiones Mathematicae Graph Theory, 2021.

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CAMERON, K.; CHAPLICK, S.; HOÀNG, C. T. Edge intersection graphs of L-shaped paths in grids. Discrete Applied Mathematics, v. 210, p. 185-194, 2016.

CELA, E.; GAAR, E. Monotonic Representations of Outerplanar Graphs as Edge Intersection Graphs of Paths on a Grid. arXiv preprint arXiv:1908.01981, 2019.

FRANCIS, M. C.; LAHIRI, A. VPG and EPG bend-numbers of Halin graphs. Discrete Applied Mathematics, v. 215, p. 95-105, 2016.

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GOLUMBIC, M. C.; LIPSHTEYN, M.; STERN, M. Single bend paths on a grid have strong helly number 4: errata atque emendationes ad “edge intersection graphs of single bend paths on a grid”. Networks, v. 62, n. 2, p. 161-163, 2013.

HELDT, D.; KNAUER, K.; UECKERDT, T. Edge-intersection graphs of grid paths: the bend number. Discrete Applied Mathematics, v. 167, p. 144-162, 2014.

HELDT, D.; KNAUER, K.; UECKERDT, T. On the bend-number of planar and outerplanar graphs. Discrete Applied Mathematics, v. 179, p. 109-119, 2014.

MARINHO, L. F. S.; SILVA, K. A.; SANTOS, T. D. B2-EPG Split. Academic Journal on Computing, Engineering and Applied Mathematics, v. 4, n. 1, p. 1-7, 2023.

PERGEL, M.; RZĄŻEWSKI, P. On edge intersection graphs of paths with 2 bends. Discrete Applied Mathematics, v. 226, p. 106-116, 2017.

STERN, M.; BIEDL, T. On edge-intersection graphs of k-bend paths in grids. Discrete Mathematics & Theoretical Computer Science, v. 12, 2010.

SZWARCFITER, J. L., SOUZA, U. S., SANTOS, T. D., GOLUMBIC, M. C., & BORNSTEIN, C. F. The Complexity of Helly-B_1-EPG Graph Recognition. Discrete Mathematics & Theoretical Computer Science, 22, 2020.

Publicado

2023-12-31

Cómo citar

DIAS DOS SANTOS, Tanilson; SILVA, Kedson Alves; MARINHO, Luiz Fernando dos Santos. K-SUN PERTENECE A B2-EPG-HELLY. Observatorio Magazine, [S. l.], v. 9, n. 1, p. a25pt, 2023. DOI: 10.20873/uft.2447-4266.2023v9n1a25pt. Disponível em: https://sistemas.uft.edu.br/periodicos/index.php/observatorio/article/view/15720. Acesso em: 16 may. 2024.