Social Networking and Computational Intelligence pp 765-773 | Cite as

# A Novel Approach of Vertex Coloring Algorithm to Solve the *K*-Colorability Problem

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## Abstract

The graph theory is one among the most studied fields for research. There are several algorithms and concepts of graph theory, which is used to solve mathematical and real-world problems. Graph coloring is one of them. The graph coloring problem is a kind of NP-hard problem. Graph coloring has the capability of solving many optimization problems like air traffic management, train routes management, time table scheduling, register allocation in operating system, and many more. The vertex coloring problem can be defined if given a graph of vertices and edges; every vertex has to color in such a manner that two adjacent vertices should not have the same color, using the minimum number of colors. This paper introduced the implementation prospective of a vertex coloring algorithm based on k-colorability using recursive computation. Implemented algorithm is tested on DIMACS graph benchmarks. Result of novel method shows it has reduced execution time and improved chromatic number.

## Keywords

Vertex coloring problem Time complexity Chromatic number Graph coloring problem DIMACS Recursion## References

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