No description available.

In this thesis, we introduce the intersperse coloring problem, which is a generalized version of the hypergraph coloring problem. In the intersperse coloring problem, we seek a coloring that assigns at least l different colors to each hyperedge of the input hypergraph, where l is an input parameter of the problem. We show that the notion of intersperse coloring unifies several well-known coloring problems, in addition to the conventional graph and hypergraph coloring problems, such as the strong coloring of hypergraphs, the star coloring problem, the problem of proper coloring of graph powers, the acyclic coloring problem, and the frugal coloring problem. We also provide a number of upper and lower bounds on the intersperse coloring problem on hypergraphs in the general case. The nice thing about our general bounds is that they can be applied to all the coloring problems that are special cases of the intersperse coloring problem. In this thesis, we also propose a new model for graph and hypergraph property testing, called the symmetric model. The symmetric model is the first model that can be used for developing property testing algorithms for non-uniform hypergraphs. We also prove that there exist graph properties that have efficient property testers in the symmetric model but do not have any efficient property tester in previously-known property testing models.

In this thesis, we introduce the intersperse coloring problem, which is a generalized version of the hypergraph coloring problem. In the intersperse coloring problem, we seek a coloring that assigns at least l different colors to each hyperedge of the input hypergraph, where l is an input parameter of the problem. We show that the notion of intersperse coloring unifies several well-known coloring problems, in addition to the conventional graph and hypergraph coloring problems, such as the strong coloring of hypergraphs, the star coloring problem, the problem of proper coloring of graph powers, the acyclic coloring problem, and the frugal coloring problem. We also provide a number of upper and lower bounds on the intersperse coloring problem on hypergraphs in the general case. The nice thing about our general bounds is that they can be applied to all the coloring problems that are special cases of the intersperse coloring problem. In this thesis, we also propose a new model for graph and hypergraph property testing, called the symmetric model. The symmetric model is the first model that can be used for developing property testing algorithms for non-uniform hypergraphs. We also prove that there exist graph properties that have efficient property testers in the symmetric model but do not have any efficient property tester in previously-known property testing models.

Thesis (Ph. D.)--University of Hong Kong, 2002. / Includes bibliographical references.

No description available.

The objective of this creative project was to create a series of cast bronze sculptures that would provide a ground for the exploration of metal patination, a chemical coloration of a metal surface. These bronzes were created using a ceramic shell investment mold and lost-wax cast in the Department of Art foundry facilities. Some of the pieces were cast in parts and either welded together or cold connected by drilling and pinning. Using recipes for hot and cold patinas, chemicals were applied to the bronze surface using a variety of application techniques, resulting in a subtle variation of warm and cool, transparent and opaque colors and tones. / Department of Art

Afhandling - Copenhagen. / Summary in Danish.

The theory of Dvořák et al. shows that a 4-critical triangle-free graph embedded in the torus has only a bounded number of faces of length greater than 4 and that the size of these faces is also bounded. We study the natural reduction in such embedded graphs-identification of opposite vertices in 4-faces. We give a computer-assisted argument showing that there are exactly four 4-critical triangle-free irreducible toroidal graphs in which this reduction cannot be applied without creating a triangle. Using this result we demonstrate several properties that are necessary for every triangle-free graph embedded in the torus to be 4-critical. Most importantly we demonstrate that every such graph has at most four 5-faces, or a 6-face and two 5-faces, or a 7-face and a 5-face, in addition to at least seven 4-faces.

Given an n-vertex graph Gand two positive integers d, k is an element of N, the (d, kn)-differential coloring problem asks for a coloring of the vertices of G(if one exists) with distinct numbers from 1 to kn(treated as colors), such that the minimum difference between the two colors of any adjacent vertices is at least d. While it was known that the problem of determining whether a general graph is (2, n)-differential colorable is NP-complete, our main contribution is a complete characterization of bipartite, planar and outerplanar graphs that admit (2, n)-differential colorings. For practical reasons, we also consider color ranges larger than n, i.e., k > 1. We show that it is NP-complete to determine whether a graph admits a (3, 2n)-differential coloring. The same negative result holds for the (left perpendicular 2n/3 right pendicular, 2n)-differential coloring problem, even in the case where the input graph is planar.

Vertex-distinguishing edge-colorings (vdec colorings) are a restriction of proper edge-colorings. These special colorings require that the sets of edge colors incident to every vertex be distinct. This is a relatively new field of study. We present a survey of known results concerning vdec colorings. We also define a new matrix which may be used to study vdec colorings, and examine its properties. We find several bounds on the eigenvalues of this matrix, as well as results concerning its determinant, and other properties. We finish by examining related topics and open problems.