Research Statement 1.1 Special Graphs

Monochromatic subgraphs of 2-edge-colored graphs

Lehel conjectured that for all n, any 2-edge-coloring of Kn admits a partition of the vertex set into a red cycle and a blue cycle. This conjecture led to a significant amount of work on related questions and was eventually proven for all n by Bessy and Thomassé. Balogh, Barát, Gerbner, Gyárfás, and Sárközy conjectured a stronger statement for large n: that if δ(G) > 3n/4, then any 2-edge-color...

An Integer Programming Model and a Tabu Search Algorithm to Generate α-labeling of Special Classes of Quadratic Graphs

First, an integer programming model is proposed to find an α-labeling for quadratic graphs. Then, a Tabu search algorithm is developed to solve large scale problems. The proposed approach can generate α-labeling for special classes of quadratic graphs, not previously reported in the literature. Then, the main theorem of the paper is presented. We show how a problem in graph theory c...

α Valuations of Special Classes of Quadratic Graphs

GraphDB: Modeling and Querying Graphs in Databases

We propose a data model and query language that integrates an explicit modeling and querying of graphs smoothly into a standard database environment. For standard applications, some key features of object-oriented modeling are offered such as object classes organized into a hierarchy, object identity, and attributes referencing objects. Querying can be done in a familiar style with a derive sta...

Complement of Special Chordal Graphs and Vertex Decomposability

In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.