Addressing scheduling problems with the best graph coloring algorithm has always been very challenging. However, university timetable problem can be formulated as a where courses are represented vertices and presence of common students or teachers corresponding edges. After that, stands to color lowest possible colors. In order accomplish this task, paper presents comparative study use in sched...

We introduce a variant of the graph coloring problem, which we denote as Budgeted Coloring Problem (BCP). Given G, an integer c and ordered list integers (b1,b2,…,bc), BCP asks whether there exists proper G where i-th color is used to at most bi many vertices. This problem generalizes two well-studied problems, Bounded (BoCP) Equitable (ECP) in case other NP-hard even for constant values c. So ...

In this paper, author uses set theory to construct a logic model of abstract figure from binary relation. Based on the uniform quantified structure, author gives two logic system for graph traversal and graph coloring respectively, moreover shows a new method of cutting graph. Around this model, there are six algorithms in this paper including exact graph traversal, Algebra calculation of natur...

We show that obtaining the lexicographically first four coloring of a planar graph is NP–hard. This shows that planar graph four-coloring is not self-reducible, assuming P 6= NP . One consequence of our result is that the schema of [JVV 86] cannot be used for approximately counting the number of four colorings of a planar graph. These results extend to planar graph k-coloring, for k ≥ 4. Resear...

The problem of reducing interference in wireless networks is becoming increasingly important with the continuous deployment of larger and more sophisticated wireless networks. In this report we analyze the interference problem from a graph theoretical viewpoint. The interference reduction problem is modeled as a graph coloring problem. However, additional constraints to graph coloring scenarios...

In Vertex Coloring Problems, one is required to assign a color to each vertex of an undirected graph in such a way that adjacent vertices receive different colors, and the objective is to minimize the cost of the used colors. In this work we solve four different coloring problems formulated as Maximum Weight Stable Set Problems on an associated graph. We exploit the transformation proposed by C...

In Vertex Coloring Problems, one is required to assign a color to each vertex of an undirected graph in such a way that adjacent vertices receive different colors, and the objective is to minimize the cost of the used colors. In this work we solve four different coloring problems formulated as Maximum Weight Stable Set Problems on an associated graph. We exploit the transformation proposed by C...