Graphs whose vertices of degree at least 2 lie in a triangle
A pendant vertex is one of degree one and an isolated vertex has degree zero. A neighborhood star-free (NSF for short) graph is one in which every vertex is contained in a triangle except pendant vertices and isolated vertices. This class has been considered before for several contexts. In the present paper, we study the complexity of the dominating induced matching (DIM) problem and the perfect edge domination (PED) problem for NSF graphs. We prove the corresponding decision problems are NP-Complete for several of its subclasses. As an added value of this study, we show three connected variants of planar positive 1in3SAT are also NP-Complete. Since these variants are more basic in complexity theory context than many graph problems, these results can be useful to prove that other problems are NP-Complete.
Authors
- Min Chih Lin (ORCID: https://orcid.org/0000-0002-5754-9761)
- Veronica A. Moyano
- Abílio Lucena (ORCID: https://orcid.org/0000-0001-6627-7692)
- Nelson Maculan (ORCID: https://orcid.org/0000-0002-3897-3356)
- Jayme Luiz Szwarcfiter
- Vinicius do Forte
Publication Details
- Journal
- RAIRO. Operations research
- Published
- 2024-10-17
- DOI
- https://doi.org/10.1051/ro/2024198
- Primary Topic
- Advanced Graph Theory Research
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Consejo Nacional de Investigaciones Científicas y Técnicas
- Conselho Nacional de Desenvolvimento Científico e Tecnológico
- Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro
- Universidad de Buenos Aires
- Fundação Coordenação de Projetos, Pesquisas e Estudos Tecnológicos
- Secretaria de Ciencia y Tecnica, Universidad de Buenos Aires
- Secretaría de Ciencia y Técnica, Universidad de Buenos Aires