http://repositorio.ufc.br/handle/riufc/64 2026-04-23T20:39:47Z 2026-04-23T20:39:47Z Camargo, Fernanda Ester Camillo http://repositorio.ufc.br/handle/riufc/71149 2023-03-07T19:20:01Z 2006-11-01T00:00:00Z

Título: Subvariedades de tipo espaço com curvatura escalar constante em espaços-forma semi-Riemannianos Autor(es): Camargo, Fernanda Ester Camillo Abstract: In this work, we obtain some results about spacelike submanifolds with constant scalar curvature in semi-Riemannian space forms, using a Simons type formula and a differential operator introduced by Cheng-Yau. In order to achieve this we impose some conditions either on the length of the second fundamental form, or on the sectional curvatures or for the mean curvature vector. The results for complete (non-compact) and compact submanifolds were obtained separately. Tipo: Tese

2006-11-01T00:00:00Z Silva, Ana Shirley Ferreira da http://repositorio.ufc.br/handle/riufc/71148 2023-03-07T19:19:53Z 2010-11-24T00:00:00Z

Título: O número b-cromático de alguns gráficos em forma de árvore Autor(es): Silva, Ana Shirley Ferreira da Abstract: A vertex colouring of a graph G is called a b-colouring if each colour class contains at least one vertex that has a neighbour in all other colour classes. The b-chromatic number χb(G) of G is the largest integer k for which G has a b-colouring with k colours. These concepts have been introduced by Irving and Manlove in 1999. They allow the analisys of the performance of some algorithms for colouring. Irving and Manlove showed that finding the b-chromatic number is NPhard for general graphs, while it can be found in polynomial time for trees. A question that naturally arises is to investigate the graphs that have a “tree structure”, for instance: cactus, chordal graphs, series-parallel graphs, block graphs, etc. In this thesis, we generalize the result of Irving and Manlove for cacti with “m-degree” at least 7 and for outerplanar graphs with girth at least 8. (The m-degree m(G) is the largest integer d such that G has at least d vertices of degree at least d − 1.) We prove a similar result for the cartesian product of a tree by a path, a cycle or a star. Regarding graphs whose blocks are cliques, we show that the fixed-parameter problem can be solved in polynomial time and we present cases where the decision problem can be solved. However, we found that the difference m(G) − χb(G) can be arbitrarily large for block graphs, which shows that the tree structure is not sufficient for having χb(G) ≥ m(G) − 1. Tipo: Tese

2010-11-24T00:00:00Z