Abstract
Similar to the tree-width (twd), the clique-width (cwd) is an invariant of graphs. There is a well-known relationship between the tree-width and clique-width for any graph. The tree-width of a special class of graphs called polygonal trees is 2, so the clique-width for those graphs is smaller or equal than 6. In this paper we show that we can improve this bound to 5 and we present a polynomial time algorithm which computes the 5-expression.
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
Courcelle, B., Engelfriet, J., Rozenberg, G.: Handle-rewriting hypergraph grammars. J. Comput. Syst. Sci. 46(2), 218–270 (1993)
Fellows, M.R., Rosamond, F.A., Rotics, U., Szeider, S.: Clique-width is NP-complete. SIAM J. Disc. Math. 23(2), 909–939 (2009)
Oum, S.I., Seymour, P.: Approximating clique-width and branch-width. J. Comb. Theory Ser. B 96(4), 514–528 (2006)
Langer, A., Reidl, F., Rossmanith, P., Sikdar, S.: Practical algorithms for MSO model-checking on tree-decomposable graphs. Comput. Sci. Rev. 1314, 39–74 (2014)
Fomin, F.V., Golovach, P.A., Lokshtanov, D., Saurabh, S.: Intractability of clique-width parameterizations. SIAM J. Comput. 39(5), 1941–1956 (2010)
Corneil, D.G., Rotics, U.: On the relationship between clique-width and treewidth. In: Brandstädt, A., Le, V.B. (eds.) WG 2001. LNCS, vol. 2204, pp. 78–90. Springer, Heidelberg (2001). doi:10.1007/3-540-45477-2_9
Golumbic, M.C., Rotics, U.: On the clique—width of perfect graph classes. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds.) WG 1999. LNCS, vol. 1665, pp. 135–147. Springer, Heidelberg (1999). doi:10.1007/3-540-46784-X_14
Corneil, D.G., Habib, M., Lanlignel, J.-M., Reed, B., Rotics, U.: Polynomial-time recognition of clique-width \(\le 3\) graphs. Disc. Appl. Math. 160(6), 834–865 (2012). Fourth Workshop on Graph Classes, Optimization, and Width Parameters Bergen, Norway, October 2009 Bergen 09
Gurski, F.: Graph operations on clique-width bounded graphs. CoRR, abs/cs/0701185 (2007)
Johansson, Ö.: Clique-decomposition, NLC-decomposition, and modular decomposition - relationships and results for random graphs. Congr. Numer. 132, 39–60 (1998)
Gurski, F., Wanke, E.: The tree-width of clique-width bounded graphs without Kn,n. In: Brandes, U., Wagner, D. (eds.) WG 2000. LNCS, vol. 1928, pp. 196–205. Springer, Heidelberg (2000). doi:10.1007/3-540-40064-8_19
Wagner, S., Gutman, I.: Maxima and minima of the Hosoya index and themerrifield-simmons index. Acta Applicandae Math. 112(3), 323–346 (2010)
Gutman, I.: Extremal hexagonal chains. J. Math. Chem. 12(1), 197–210 (1993)
Harary, F., NATO Advanced Study Institute: Graph Theory and Theoretical Physics. Academic Press, London (1967)
Courcelle, B., Olariu, S.: Upper bounds to the clique width of graphs. Discrete Appl. Math. 101, 77–114 (2000)
Acknowledgment
The author would like to thank CONACYT for the scholarship granted in pursuit of his doctoral studies. This work has been supported by the Cuerpo acadmico of Algoritmos Combinatorios and Aprendizaje (CA-BUAP-257) of the BUAP.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
González-Ruiz, J.L., Marcial-Romero, J.R., Hernández, J.A., De Ita, G. (2017). Computing the Clique-Width of Polygonal Tree Graphs. In: Pichardo-Lagunas, O., Miranda-Jiménez, S. (eds) Advances in Soft Computing. MICAI 2016. Lecture Notes in Computer Science(), vol 10062. Springer, Cham. https://doi.org/10.1007/978-3-319-62428-0_36
Download citation
DOI: https://doi.org/10.1007/978-3-319-62428-0_36
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-62427-3
Online ISBN: 978-3-319-62428-0
eBook Packages: Computer ScienceComputer Science (R0)