Kumar N . Sivarajan and Robert J . McEliece, California Institute of Technology,’ and John W. Ketchum, GTE Laboratories Incorporated. In this paper, we describe some heuristic channel assignment algorithms for cellular systems, that we have recently developed. These algorithms have yielded optimal, or near-optimal assignments, in many cases. The channel assignment problem can be viewed as a gen...

We first present a literature review of heuristics and metaheuristics developed for the problem of coloring graphs. We then present a Greedy Randomized Adaptive Search Procedure (GRASP) for coloring sparse graphs. The procedure is tested on graphs of known chromatic number, as well as random graphs with edge probability 0.1 having from 50 to 500 vertices. Empirical results indicate that the pro...

Unit disk graphs are the intersection graphs of equal sized circles in the plane. In this paper, we consider the maximum independent set problems on unit disk graphs. When the given unit disk graph is de ned on a slab whose width is k, we propose an algorithm for nding a maximum independent set in O(n 4 d 2k= p 3 e ) time where n denotes the number of vertices. We also propose a (1 1=r)-approxi...

The problem of online coloring an unknown graph is known to be hard. Here we consider the problem of online coloring in the relaxed situation where the input must be isomorphic to a given known graph. All that foils a computationally powerful player is that it is not known to which sections of the graph the vertices to be colored belong. We show that the performance ratio of any online coloring...

This thesis studies both several extremal problems about coloring of graphs and a labeling problem on graphs. We consider colorings of graphs that are either embeddable in the plane or have low maximum degree. We consider three problems: coloring the vertices of a graph so that no adjacent vertices receive the same color, coloring the edges of a graph so that no adjacent edges receive the same ...

a proper vertex coloring of a simple graph is $k$-forested if the graph induced by the vertices of any two color classes is a forest with maximum degree less than $k$. a graph is $k$-forested $q$-choosable if for a given list of $q$ colors associated with each vertex $v$, there exists a $k$-forested coloring of $g$ such that each vertex receives a color from its own list. in this paper, we prov...

The graph coloring problem is a practical method of representing many real world problems including time scheduling, frequency assignment, register allocation, and circuit board testing. The most important fact that makes graph coloring exciting is that finding the minimum number of colors for an arbitrary graph is NP-hard. This project implements combinatorial optimization algorithms (genetic ...

Let G = (V,E) be a simple and connected graph. The graph coloring problem on G is to color the vertices of G such that the colors of any two adjacent vertices are different and the number of used colors is as small as possible. By assigning a positive integer to a color, the sum coloring problem asks the minimum sum of the coloring numbers assigned for all vertices. In this paper, we introduce ...

In the edge precoloring extension problem we are given a graph with some of the edges having a preassigned color and it has to be decided whether this coloring can be extended to a proper k-edge-coloring of the graph. In list edge coloring every edge has a list of admissible colors, and the question is whether there is a proper edge coloring where every edge receives a color from its list. We s...

The Coloring problem is to test whether a given graph can be colored with at most k colors for some given k, such that no two adjacent vertices receive the same color. The complexity of this problem on graphs that do not contain some graph H as an induced subgraph is known for each fixed graph H. A natural variant is to forbid a graph H only as a subgraph. We call such graphs strongly H-free an...