The main aim of this paper consists in developing an effective e-learning tool, focused on evolutionary algorithms, in order to solve the graph coloring problem. Subsidiary, we apply graph coloring for register allocation in embedded systems. From didactic viewpoint, our tool has benefits in the learning process because it helps students to observe the relationship between the graph coloring pr...

An edge-coloring of a graph G with natural numbers is called a sum edge-coloring if the colors of edges incident to any vertex of G are distinct and the sum of the colors of the edges of G is minimum. The edge-chromatic sum of a graph G is the sum of the colors of edges in a sum edge-coloring of G. It is known that the problem of finding the edge-chromatic sum of an r-regular (r ≥ 3) graph is N...

The graph coloring problem (GCP) is one of the most interesting, studied and difficult combinatorial optimization problems. That is why, several approaches were developed for solving this problem, including exact approaches, heuristic approaches, metaheuristics and hybrid approaches. In this paper, we try to solve the graph coloring problem using a new approach based on the quantum inspired cuc...

<span lang="EN-US">This research focuses on an analysis of different algorithms for the graph vertex coloring problem. Some approaches to solving problem are discussed. Moreover, some studies and several methods its solution analyzed as well. An exact algorithm (using backtracking method) is presented. The complexity Determining average execution time consistent with multitasking mode ope...

We study the complexity of several coloring problems on graphs, parameterized by the treewidth t of the graph: (1) The list chromatic number χl(G) of a graph G is defined to be the smallest positive integer r, such that for every assignment to the vertices v of G, of a list Lv of colors, where each list has length at least r, there is a choice of one color from each vertex list Lv yielding a pr...

A new variation of the coloring problem, μ-coloring, is defined in this paper. Given a graph G and a function μ, a μ-coloring is a coloring where each vertex v of G must receive a color at most μ(v). It is proved that μ-coloring lies between coloring and list-coloring, in the sense of generalization of problems and computational complexity. The notion of perfection is extended for μ-coloring, l...