the prevalent communications networks suffer from lack of spectrum and spectrum inefficiency. this has motivated researchers to develop cognitive radio (cr) as a smart and dynamic radio access promised solution. a major challenge to this new technology is how to make fair assignment of available spectrum to unlicensed users, particularly for smart grids communication. this paper introduces an i...

Vertex coloring of a graph is the assignment of labels to the vertices of the graph so that adjacent vertices have different labels. In the case of polyhedral graphs, the chromatic number is 2, 3, or 4. Edge coloring problem and face coloring problem can be converted to vertex coloring problem for appropriate polyhedral graphs. We have been developed an interactive learning system of polyhedra,...

let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

In this note, we use a reduction by Cornaz and Jost from the graph (max-)coloring problem to the maximum (weighted) stable set problem in order to characterize new graph classes where the graph coloring problem and the more general max-coloring problem can be solved in polynomial time.

In the minimum sum coloring problem, the goal is to color the vertices of a graph with the positive integers such that the sum of all colors is minimal. Recently, it was shown that coloring a graph by iteratively coloring maximum independent sets yields a 4 + o(1) approximation for the minimum sum coloring problem. In this note, we show that this bound is tight. We construct a graph for which t...

In a previous work, we proposed a new integer programming formulation for the graph coloring problem which, to a certain extent, avoids symmetry. We studied the facet structure of the 0/1-polytope associated with it. Based on these theoretical results, we present now a Branch-and-Cut algorithm for the graph coloring problem. Our computational experiences compare favorably with the well-known ex...

Let Γ be directed strongly connected finite graph of uniform outdegree (constant outdegree of any vertex) and let some coloring of edges of Γ turn the graph into deterministic complete automaton. Let the word s be a word in the alphabet of colors (considered also as letters) on the edges of Γ and let Γs be a mapping of vertices Γ. A coloring is called k-synchronizing if for any word t |Γt| ≥ k ...

This paper proposes a new method based on the cultural algorithm to solve graph coloring problem (GCP). Graph coloring problem involves finding the minimum number of colors for coloring the graph vertices such that adjacent vertices have distinct colors. In this paper various components of cultural algorithm have been implemented to solve GCP with a self adaptive behavior in an efficient manner...