A proper edge-coloring of a given undirected graph with natural numbers identified with colors is an interval (or consecutive) coloring if the colors of edges incident to each vertex form an interval of consecutive integers. Not all graphs admit such an edge-coloring and the problem of deciding whether a graph is interval colorable is NP-complete. For a graph that is not interval colorable, det...

As is well known, the frequency allocation problem for mobile telephone networks can be approximated by a graph coloring problem where vertices model transmitters, colors model frequencies, and an edge corresponds to a pair of transmitters that must not use the same frequency. However, the graph coloring analogy doesn't suuce for modeling real world problems , which involve soft constraints and...

The max-coloring problem is to compute a legal coloring of the vertices of a graph G = (V,E) with vertex weights w such that ∑k i=1 maxv∈Ci w(vi) is minimized, where C1, . . . , Ck are the various color classes. For general graphs, max-coloring is as hard as the classical vertex coloring problem, a special case of the former where vertices have unit weight. In fact, in some cases it can even be...

In this paper we initiate a systematic study of a problem that has the flavor of two classical problems, namely Coloring and Domination, from the perspective of algorithms and complexity. A dominator coloring of a graph G is an assignment of colors to the vertices of G such that it is a proper coloring and every vertex dominates all the vertices of at least one color class. The minimum number o...

The problem of edge coloring a bipartite graph is to color the edges so that adjacent edges receive di erent colors An optimal algorithm uses the minimum number of colors to color the edges We consider several approximation algorithms for edge coloring bipartite graphs and show tight bounds on the number of colors they use in the worst case We also present results on the constrained edge colori...

In this paper, we study the sub-coloring and hypo-coloring problems on interval graphs. These problems have applications in job scheduling and distributed computing and can be used as “subroutines” for other combinatorial optimization problems. In the sub-coloring problem, given a graph G, we want to partition the vertices of G into minimum number of sub-color classes, where each sub-color clas...

Motivated by the frequency assignment problem in heterogeneous multihop radio networks, where different radio stations may have different transmission ranges, we introduce two new types of coloring of graphs, which generalize the well-known Distance-k-Coloring. Let G = (V,E) be a graph modeling a radio network, and assume that each vertex v of G has its own transmission radius r(v), a nonnegati...

Cognitive radio networks spectrum access, which allows secondary users opportunistically access unused licensed channels to exploit instantaneous spectrum availability, is a promising approach to achieve efficient spectrum utilization and mitigate spectrum scarcity. In order to reduce spectrum handoff overhead, this paper propose two heuristic spectrum allocation and reallocation methods based ...

Graph anticoloring problem is partial coloring problem where the main feature is the opposite rule of the graph coloring problem, i.e., if two vertices are adjacent, their assigned colors must be the same or at least one of them is uncolored. In the same way, Berge in 1972 proposed the problem of placing b black queens and w white queens on a n× n chessboard such that no two queens of different...

The vertex coloring of graphs is a well-known graphs. In this coloring, all the vertices are assigned colors in such way that no two adjacent have same color. We can call type P2 where path graph. However, there situations which cannot give us solution to problem at hand. To answer questions, article, we introduce novel graph called P3 coloring. A P3-colorable if assign every distinct. minimum ...