the robust coloring problem (rcp) is a generalization of the well-known graph coloring problem where we seek for a solution that remains valid when extra edges are added. the rcp is used in scheduling of events with possible last-minute changes and study frequency assignments of the electromagnetic spectrum. this problem has been proved as np-hard and in instances larger than 30 vertices, meta-...

The Robust Coloring Problem (RCP) is a generalization of the well-known Graph Coloring Problem where we seek for a solution that remains valid when extra edges are added. The RCP is used in scheduling of events with possible last-minute changes and study frequency assignments of the electromagnetic spectrum. This problem has been proved as NP-hard and in instances larger than 30 vertices, meta-...

In this chapter a new formulation of the robust graph coloring problem (RGCP) is proposed. In opposition to classical GCP defined for the given graph G(V,E) not only elements of E but also Ē can be subject of color conflicts in edge vertices. Conflicts in Ē are assigned penalties 0<P(e)<1. In addition to satisfying constraints related to the number of colors and/or a threshold of the acceptable...

This paper studies the Robust Coloring Problem (RCP), a variant of the Minimal Coloring Problem which maintains the number of colors fixed. In this problem, two non-adjacent vertex that have the same color are penalized. The sum of penalties of a coloring is called rigidity level. To solve the RCP, an Iterated Local Search (ILS) algorithm using the Random Variable Neighborhood Descent (RVND) lo...

given a graph $g$, the total dominator coloring problem seeks aproper coloring of $g$ with the additional property that everyvertex in the graph is adjacent to all vertices of a color class. weseek to minimize the number of color classes. we initiate to studythis problem on several classes of graphs, as well as findinggeneral bounds and characterizations. we also compare the totaldominator chro...

A fuzzy graph is a symmetric binary fuzzy relation on a fuzzy subset. The concept of fuzzy sets and fuzzy relations was introduced by L.A.Zadeh in 1965cite{zl} and further studiedcite{ka}. It was Rosenfeldcite{ra} who considered fuzzy relations on fuzzy sets and developed the theory of fuzzy graphs in 1975. The concepts of fuzzy trees, blocks, bridges and cut nodes in fuzzy graph has been studi...

applying robust optimization to solve product mix problem in automotive industries in this article, applying robust optimization in product mix problem in automotive industries is presented. the problem includes determining both the quantity and the identification of each product to produce to maximize profit. at first, the deterministic model will be presented. then, robust model of product mi...