Abstract
A novel method to model the 3-coloring on polygonal tree graphs is presented. This proposal is based on the logical specification of the constraints generated for a valid 3-coloring on polygonal graphs. In order to maintain a polynomial time procedure, the logical constraints are formed in a dinaymic way. At the same time, the graph is traversing in postorder, resulting in a polynomial time instance of the incremental satisfiability problem. This proposal can be extended for considering other polynomial time instances of the 3-coloring problem.
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
Byskov, J.M.: Exact algorithms for graph colouring and exact satisfiability. Ph.D. thesis, University of Aarbus, Denmark (2005)
De Ita, G., Marcial-Romero, R., Lopez, P., Gonzalez, M.: Linear-time algorithms for computing the Merrifield-Simmons index on polygonal trees. MATCH Commun. Math. Comput. Chem. 79(1), 55–78 (2018)
Došlić, T., Måløy, F.: Chain hexagonal cacti: matchings and independent sets. Discret. Math. 310, 1676–1690 (2010)
Dvor̃ák, Z., Král, D., Thomas, R.: Three-coloring triangle-free graphs on surfaces. In: Proceedings of 20th ACM-SIAM Symposium on Discrete Algorithms, pp. 120–129 (2009)
Mertzios, G.B., Spirakis, P.G.: Algorithms and almost tight results for 3-colorability of small diameter graphs. Technical report (2012). arxiv.org/pdf/1202.4665v2.pdf
Mouhoub, M., Sadaoui, S.: Systematic versus non systematic methods for solving incremental satisifiability. Int. J. Artif. Intell. Tools 16(1), 543–551 (2007)
Stacho, J.: 3-colouring AT-free graphs in polynomial time. In: Cheong, O., Chwa, K.-Y., Park, K. (eds.) ISAAC 2010. LNCS, vol. 6507, pp. 144–155. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17514-5_13
Shiu, W.C.: Extremal Hosoya index and Merrifield-Simmons index of hexagonal spiders. Discret. Appl. Math. 156, 2978–2985 (2008)
Wagner, S., Gutman, I.: Maxima and minima of the Hosoya index and the Merrifield-Simmons index. Acta Applicandae Mathematicae 112(3), 323–346 (2010)
Wieringa, S.: Incremental satisfiability solving and its applications. Ph.D. thesis, Department of Computer Science and Engineering, Alto University (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
López-Ramírez, C., De Ita, G., Neri, A. (2018). Modelling 3-Coloring of Polygonal Trees via Incremental Satisfiability. In: Martínez-Trinidad, J., Carrasco-Ochoa, J., Olvera-López, J., Sarkar, S. (eds) Pattern Recognition. MCPR 2018. Lecture Notes in Computer Science(), vol 10880. Springer, Cham. https://doi.org/10.1007/978-3-319-92198-3_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-92198-3_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-92197-6
Online ISBN: 978-3-319-92198-3
eBook Packages: Computer ScienceComputer Science (R0)