1Assistant Professor, Department of Mathematics, Srimad Andavan Arts and Science College (Autonomous) No.7, Nelson Road, T.V. Kovil, Trichy, Tamilnadu, India-620005. E-mail: andavanmathsramesh@gmail.com
2Assistant Professor, Kongunadu College of Engineering and Technology, Tholurpatti, Hottiam. E-mail: kavipraba18@gmail.com
*Corresponding Author: Dr. A. Rameshkumar, Head & Research Adviser, Department of Mathematics, Srimad Andavan Arts and Science College (Autonomous), No.7, Nelson Road, T.V. Kovil, Trichy, Tamilnadu, India-620005. E-mail: andavanmathsramesh@gmail.com
Mathematical Subject Classification: 05C15
The main result of the paper is that in practically interesting situations determining the optimal number of colors in the proposed coloring is an NP-hard problem. A possible conclusion to draw from this result is that for practical transitive tournament search algorithms we have to develop approximate greedy coloring algorithms. It is an empirical fact that coloring the nodes of a graph can be used to speed up clique search algorithms. In directed graphs transitive sub tournaments can play the role of cliques. In order to speed up algorithms to locate large transitive tournaments we propose a scheme for coloring the nodes of a directed graph.
Directed graph, tournament, Graph coloring, NP-hard problem
