Abstract
Treewidth and pathwidth are important graph parameters that represent how close the graph is to trees and paths respectively. We calculate treewidth and pathwidth on parameterized chordal and threshold graphs. We define a chordal + 1v graph as a graph that can be made into a chordal graph by removing a vertex. We give polynomial time algorithms for computing the treewidth of a chordal + 1v graph, pathwidth of a threshold + 1v graph and a threshold + 2e graph. The mixed search number of a graph is the minimum number of cops required to capture a single robber, who is hiding in the graph. We apply the algorithm to compute the pathwidth in order to compute the mixed search number of a threshold + 1v graph.
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
Preview
Unable to display preview. Download preview PDF.
References
Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in a k-tree. SIAM J. Algebraic Discrete Methods 8(2), 277–284 (1987)
Bodlaender, H.L.: A tourist guide through treewidth. Acta Cybernetica 11, 1–21 (1993)
Bodlaender, H.L.: Treewidth: Characterizations, applications, and computations. In: Fomin, F.V. (ed.) WG 2006. LNCS, vol. 4271, pp. 1–14. Springer, Heidelberg (2006)
Cai, L.: Parameterized complexity of vertex colouring. Discrete Appl. Math. 127(3), 415–429 (2003)
Sai Krishna, D., Thirumala Reddy, T.V., Sai Shashank, B., Pandu Rangan, C.: Pathwidth and searching in parameterized threshold graphs (to appear in LNCS) (2010), http://www.cse.iitm.ac.in/~dsaikris/Site/Research_files/psptg_full.pdf
Flocchini, P., Huang, M.J., Luccio, F.L.: Contiguous search in the hypercube for capturing an intruder. IPDPA 01, 62 (2005)
Flum, J., Grohe, M.: Parameterized Complexity Theory, 1st edn. Texts in Theoretical Computer Science. An EATCS Series. Springer, Heidelberg (2006)
Fomin, F.V., Heggernes, P., Mihai, R.: Mixed search number and linear-width of interval and split graphs. In: Brandstädt, A., Kratsch, D., Müller, H. (eds.) WG 2007. LNCS, vol. 4769, pp. 304–315. Springer, Heidelberg (2007)
Fomin, F.V., Thilikos, D.M.: An annotated bibliography on guaranteed graph searching. Theor. Comput. Sci. 399(3), 236–245 (2008)
Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Annals of Discrete Mathematics, vol. 57. North-Holland Publishing Co., Amsterdam (2004)
Heggernes, P., Mihai, R.: Mixed search number of permutation graphs. In: Preparata, F.P., Wu, X., Yin, J. (eds.) FAW 2008. LNCS, vol. 5059, pp. 196–207. Springer, Heidelberg (2008)
LaPaugh, A.S.: Recontamination does not help to search a graph. J. ACM 40(2), 224–245 (1993)
Lozin, V.V., Milanic, M.: Tree-width and optimization in bounded degree graphs. In: Graph-Theoretic Concepts in Computer Science, 32nd International Workshop, WG, Bergen, Norway, June 22-24, Revised Papers, pp. 45–54 (2007)
Mahadev, N.V.R., Peled, U.N.: Threshold graphs and related topics. Annals of Discrete Mathematics, vol. 56. Elsevier Science Publishers B.V., North Holland, Amsterdam (1995)
Mancini, F.: Minimum fill-in and treewidth of split+ke and split+kv graphs. In: Tokuyama, T. (ed.) ISAAC 2007. LNCS, vol. 4835, pp. 881–892. Springer, Heidelberg (2007)
Marx, D.: Parameterized coloring problems on chordal graphs. Theor. Comput. Sci. 351(3), 407–424 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Krishna, D.S., Reddy, T.V.T., Shashank, B.S., Rangan, C.P. (2010). Pathwidth and Searching in Parameterized Threshold Graphs. In: Rahman, M.S., Fujita, S. (eds) WALCOM: Algorithms and Computation. WALCOM 2010. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11440-3_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-11440-3_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11439-7
Online ISBN: 978-3-642-11440-3
eBook Packages: Computer ScienceComputer Science (R0)