This paper describes an exact algorithm for the Equitable Coloring Problem, based on the well known DSatur algorithm for the classic Coloring Problem with new pruning rules specifically derived from the equity constraint. Computational experiences show that our algorithm is competitive with those known in literature.

For example is a chromatic number with the smallest integer so that graph has true vertex coloring k color. Chromatic still an interesting study which being studied for its development through coloring. Graph special case of labeling. Labeling here means, giving color to points at certain limit no two vertices have same This aims calculate in several classes graphs including , Based on results ...

I propose to develop a deterministic parallel framework for performing iterative computation on a graph which schedules work on vertices based upon a valid coloring. Preliminary work modifying Graphlab, a parallel framework for implementing iterative machine learning algorithms on data graphs, has demonstrated the merits of this approach by improving performance and eliminating non-determinism....

A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, such that no two adjacent or incident elements receive the same color. Let L(x) be a set of colors assigned to each element x of G. Then a list total coloring of G is a total coloring such that each element x receives a color contained in L(x). The list total coloring problem asks whether G has a list tot...

Grouping problems aim to partition a set of items into multiple mutually disjoint subsets according to some specific criterion and constraints. Grouping problems cover a large class of important combinatorial optimization problems that are generally computationally difficult. In this paper, we propose a general solution approach for grouping problems, i.e., reinforcement learning based local se...

OBJECTIVES Hair coloring products are widely used and contain components that are mutagenic and carcinogenic. An association between occupational exposure to hair coloring products and hematopoietic cancers has been reported, but the risk for these cancers among users has not been carefully evaluated. METHODS We conducted a population-based, case-control study with telephone interviews from 3...

Constraint satisfaction research has focussed on consistency checking using k-consistency and its variations such as arc-consistency, and path-consistency. We define a new form of consistency checking that is based on coloring the micro-structure graph of a constraint satisfaction problem (CSP). In our formulation, if the micro-structure graph of a CSP with n variables can be colored with n − 1...