Convexities convexities of paths and geometric

• Main Author: Rafael Teixeira de AraÃjo
• Other Authors: Rudini Menezes Sampaio
• Format: Others
• Language: Portuguese
• Published: Universidade Federal do Cearà 2014
• Subjects: Convexidade em grafos; Convexidade geodÃsica; NÃmero de Hull; NÃmero de convexidade; Convexidade geomÃtrica; Convexity in graph; hull number; convexity number; P3 convexity; geodetic convexity; geometric convexity; CIENCIA DA COMPUTACAO
• Online Access: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12104

FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico === In this dissertation we present complexity results related to the hull number and the convexity number for P3 convexity. We show that the hull number and the convexity number are NP-hard even for bipartite graphs. Inspired by our research in convexity based on paths, we introduce a new convexity, where we defined as convexity of induced paths of order three or P∗ 3 . We show a relation between the geodetic convexity and the P∗ 3 convexity when the graph is a join of a Km with a non-complete graph. We did research in geometric convexity and from that we characterized graph classes under some convexities such as the star florest in P3 convexity, chordal cographs in P∗ 3 convexity, and the florests in TP convexity. We also demonstrated convexities that are geometric only in specific graph classes such as cographs in P4+-free convexity, F free graphs in F-free convexity and others. Finally, we demonstrated some results of geodesic convexity and P∗ 3 in graphs with few P4âs. === In this dissertation we present complexity results related to the hull number and the convexity number for P3 convexity. We show that the hull number and the convexity number are NP-hard even for bipartite graphs. Inspired by our research in convexity based on paths, we introduce a new convexity, where we defined as convexity of induced paths of order three or P∗ 3 . We show a relation between the geodetic convexity and the P∗ 3 convexity when the graph is a join of a Km with a non-complete graph. We did research in geometric convexity and from that we characterized graph classes under some convexities such as the star florest in P3 convexity, chordal cographs in P∗ 3 convexity, and the florests in TP convexity. We also demonstrated convexities that are geometric only in specific graph classes such as cographs in P4+-free convexity, F free graphs in F-free convexity and others. Finally, we demonstrated some results of geodesic convexity and P∗ 3 in graphs with few P4âs.