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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Gamache M, Hertz A, Ouellet JO (2007) A graph coloring model for a feasibility problem in monthly crew scheduling with preferential bidding. Comput Oper Res 34(8):2384–2395
Zufferey N, Amstutz P, Giaccari P (2008) Graph colouring approaches for a satellite range scheduling problem. J Sched 11(4):151–162
de Werra D (1985) An introduction to timetabling. European J Oper Res 19:151–162
Burke EK, McCollum B, Meisels A, Petrovic S, Qu R (2007) A graph-based hyper heuristic for timetabling problems. Eur J Oper Res 176:177–192
de Werra D, Eisenbeis C, Lelait S, Marmol B (1999) On a graph-theoretical model for cyclic register allocation. Discr Appl Math 93(2):191–203
Smith DH, Hurley S, Thiel SU (1998) Improving heuristics for the frequency assignment problem. Eur J Oper Res 107(1):76–86
Woo TK, Su SYW, Wolfe RN (2002) Resource allocation in a dynamically partitionable bus network using a graph coloring algorithm. IEEE Trans Commun 39:1794–1801
Garey MR, Johnson DS (1979) Computers and intractability. Freeman
Malaguti E, Monaci M, Toth P (2011) An exact approach for the vertex coloring problem. Discr Optim 8(2):174–190
Segundo PS (2012) A new DSATUR-based algorithm for exact vertex coloring. Comput Oper Res 39:1724–1733
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Mahajani, S., Sharma, P., Malviya, V. (2020). A Novel Approach of Vertex Coloring Algorithm to Solve the K-Colorability Problem. In: Shukla, R., Agrawal, J., Sharma, S., Chaudhari, N., Shukla, K. (eds) Social Networking and Computational Intelligence. Lecture Notes in Networks and Systems, vol 100. Springer, Singapore. https://doi.org/10.1007/978-981-15-2071-6_64
Download citation
DOI: https://doi.org/10.1007/978-981-15-2071-6_64
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-2070-9
Online ISBN: 978-981-15-2071-6
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)