Multi-coloring problem is a generalization of the well known Graph coloring problem which is known to be NP-hard. Multi-coloring problem can be solved by algorithms designed for the graph coloring problem after transformation of the graphs. However, since the graph transformations increase the size and order of the given graph, in some cases, it may be impractical to solve multi-coloring proble...

Graph Coloring Problem (GCP) is the assignment of colors to certain elements in a graph based on constraints. GCP used by assigning color label each node with neighboring nodes assigned different and minimum number used. Based this, can be drawn into an optimization problem that minimize Optimization problems coloring occur due uncertainty use used, so it assumed there colored vertices. One mat...

in this paper, a robust model presented is developed for hub covering flow problem in which hubs have capacity. this problem has two objective functions converting to a single-objective problem by using weighting method. firstly, the problem will be formulated in a certain case. then, by considering the demand as a non-random variable, it will be modeled by robust optimization. finally, by usin...

Given a graph G, an integer k, and a cost cuv associated with all pairs uv of non-adjacent vertices in G, the robust graph coloring problem is to assign a color in {1, · · · , k} to every vertex of G so that no edge has both endpoints with the same color, and the total cost of the pairs of vertices having the same color is minimum. We propose a branch and price algorithm for the solution of thi...