A Tree-Based Graph Coloring Algorithm Using Independent Set

  • Harish PatidarEmail author
  • Prasun Chakrabarti
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 714)


This paper introduces a tree data structure-based graph coloring algorithm. Algorithm explores vertices in the tree form to finds maximal independent set, than these independent sets are colored with minimum colors. Proposed algorithm is tested on various DIMACS standard of graph instances. Algorithm is design to solve graph coloring problem for high degree graphs, i.e. the proposed algorithm is highly efficient for those graphs which has number of edges to number of vertices ratio is very high. Worst and best case time complexity of proposed algorithm is also discussed in this paper.


Maximal independent set Complement edge table Graph coloring Chromatic number 


  1. 1.
    Berchtold, S., Böhm, C., Braunmüller, B., Keim, D. A., and Kriegel, H.-P.: Fast Parallel Similarity Search in Multimedia Databases, In ACM SIGMOD Int. Conf. on Management of Data, (1997)Google Scholar
  2. 2.
    Chaitin, G. J., Auslander, M. A., Chandra, A. K., Cocke, J., Hopkins, M. E., and Markstein, P. W.: Register Allocation via Coloring. Computer Languages, Vol. 6, Issue 1, (1981) 47–57Google Scholar
  3. 3.
    Mahmoudi, S., Lotfi, S.: Modified cuckoo optimization algorithm (MCOA) to solve graph coloring problem. ELSVIER, Applied Soft Computing, (2015) 48–64Google Scholar
  4. 4.
    Gupta A., Patidar H.: A Survey on Heuristic Graph Coloring Algorithm. International Journal for Scientific Research & Development, Vol. 4, Issue 04, (2016) 297–301Google Scholar
  5. 5.
    Salari, E., and Eshghi, K.: An ACO Algorithm for the Graph Coloring Problem. Interracial Journal Contemp. Math Sciences, Vol. 3, no. 6 (2008) 293–304Google Scholar
  6. 6.
    Thang, N. Bui, Nguyen, T. H., Patel, C. M., and Kim-Anh Phan, T.: An Ant-Based Algorithm for Coloring Graphs. Discrete Applied Mathematics 156 (2008) 190–200Google Scholar
  7. 7.
    Chen, B., Chen, Bo., Liu, H., Zhang X.: A Fast Parallel Genetic Algorithm for Graph Coloring Problem Based on CUDA. IEEE International Conference on Cyber-Enabled Distributed Computing and Knowledge Discovery, (2015) 145–148Google Scholar
  8. 8.
    Sabar, N. R., Ayob M., Qu, R., Kendall, G.: A Graph Coloring Constructive Hyper-Heuristic for Examination Time Tabling Problems. Online publication, Springer Science Business Media, (2011)Google Scholar
  9. 9.
    Hindi, M., and Yampolskiy, R. V.: Genetic Algorithm Applied to the Graph Coloring Problem, Proc. 23rd Midwest Artificial Intelligence and Cognitive Science Conf, (2012) 61–66Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringSir Padampat Singhania UniversityUdaipurIndia

Personalised recommendations