A proper coloring of a graph is a partition of its vertex set into stable sets, where each part corresponds to a color. For a vertex-weighted graph, the weight of a color is the maximum weight of its vertices. The weight of a coloring is the sum of the weights of its colors. Guan and Zhu defined the weighted chromatic number of a vertex-weighted graph G as the smallest weight of a proper colori...

An equitable coloring of a graph $G=(V,E)$ is (proper) vertex-coloring $G$, such that the sizes any two color classes differ by at most one. In this paper, we consider problem in block graphs. Recall latter are graphs which each 2-connected component complete graph. The remains hard class present some theoretic results relating various parameters. Then use them order to trace algorithmic implic...

Graph coloring is a well known problem from graph theory that, when solving it with local search algorithms, is typically treated as a series of constraint satisfaction problems: for a given number of colors k, one has to find a feasible coloring; once such a coloring is found, the number of colors is decreased and the local search starts again. In this article we explore the application of Ite...

This paper presents an ant system algorithm for the graph coloring problem. This ant system algorithm has several new features compared to previous ant system algorithms for the coloring problem. The main idea of the algorithm is for a colony of ants to color the graph, in which ants use its knowledge about the local neighborhood, recently visited nodes, and information stored at each vertex. F...

university course timetabling is a complex optimizationproblem. there are many components like departments, faculties, rooms,and students making the problem huge and difficult to solve. eachcomponent enforces a set of normally conflicting constraints on thesolution space. the problem will be solved if courses are scheduled indifferent rooms and within some specific time slots such that a set of...

We describe a graph coloring problem associated with the determination of mathematical derivatives. The coloring instances are obtained as intersection graphs of row partitioned sparse derivative matrices. The size of the graph is dependent on the partition and can be varied between the number of columns and the number of nonzero entries. If solved exactly our proposal will yield a significant ...

The edges of the Cartesian product of graphs G x Hare to be colored with the condition that all rectangles, i.e., K2 x K2 subgraphs, must be colored with four distinct colors. The minimum number of colors in such colorings is determined for all pairs of graphs except when G is 5-chromatic and H is 4or 5-chromatic.

This paper aims at introducing the concept of selection graph with an application to a non-trivial problem. A selection graph is made of a set of classes, each class having multiple realizations, and of an uncompatibility graph built on these realizations. Coloring a selection graph can be used to solve constrained scheduling, constrained ressource allocation, and dichotomy-based constrained en...