Abstract
We investigate graphs that can be represented as vertex intersections of horizontal and vertical paths in a grid, known as B 0-VPG graphs. Recognizing these graphs is an NP-hard problem. In light of this, we focus on their subclasses. In the paper, we describe polynomial time algorithms for recognizing chordal B 0-VPG graphs, and for recognizing B 0-VPG graphs that have a representation on a grid with 2 rows.
The authors wish to thank Krishnam Raju Jampani, Therese Biedl, and Martin Charles Golumbic for fruitful discussions in the early stages of this work.
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.
Similar content being viewed by others
References
Asinowski, A., et al.: String graphs of k-bend paths on a grid. Electronic Notes in Discrete Mathematics 37, 141–146 (2011); LAGOS 2011 - VI Latin-American Algorithms, Graphs and Optimization Symposium, http://dx.doi.org/10.1016/j.endm.2011.05.025
Asinowski, A., Cohen, E., Golumbic, M.C., Limouzy, V., Lipshteyn, M., Stern, M.: Intersection graphs of paths on a grid, technical report (2010)
Bandy, M., Sarrafzadeh, M.: Stretching a knock-knee layout for multilayer wiring. IEEE Trans. Computing 39, 148–151 (1990)
Booth, K.S., Lueker, G.S.: Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms. Journal of Computer and System Sciences 13, 335–379 (1976)
Cornelsen, S., Schank, T., Wagner, D.: Drawing graphs on two and three lines. Journal of Graph Algorithms and Applications 8, 161–177 (2004)
Fulkerson, D.R., Gross, O.A.: Incidence matrices and interval graphs. Pacific Journal of Mathematics 15, 835–855 (1965)
Golumbic, M.C.: Algorithmic graph theory and perfect graphs, 2nd edn. North-Holland (2004)
Golumbic, M.C., Ries, B.: On the intersection graphs of orthogonal line segments in the plane: characterizations of some subclasses of chordal graphs (submitted manuscript, 2011)
Haeupler, B., Jampani, K.R., Lubiw, A.: Testing simultaneous planarity when the common graph is 2-connected. In: Cheong, O., Chwa, K.-Y., Park, K. (eds.) ISAAC 2010, Part II. LNCS, vol. 6507, pp. 410–421. Springer, Heidelberg (2010)
Heckmann, R., Klasing, R., Monien, B., Unger, W.: Optimal Embedding of Complete Binary Trees into Lines and Grids. In: Schmidt, G., Berghammer, R. (eds.) WG 1991. LNCS, vol. 570, pp. 25–35. Springer, Heidelberg (1992)
Jamison, R.E., Mulder, H.M.: Constant tolerance intersection graphs of subtrees of a tree. Discrete Mathematics 290, 27–46 (2005)
Kratochvíl, J.: Personal communication
Kratochvíl, J.: String graphs II. Recognizing string graphs is NP-hard. Journal of Combinatorial Theory B 52, 67–78 (1991)
Kratochvíl, J., Matoušek, J.: Intersection graphs of segments. Journal of Combinatorial Theory Series B 62, 289–315 (1994)
Kratochvíl, J., Nešetřil, J.: Independent set and clique problems in intersection-defined classes of graphs. Commentationes Mathematicae Universitatis Carolinae 31, 85–93 (1990)
McMorris, F.R., Scheinerman, E.R.: Connectivity threshold for random chordal graphs. Graphs and Combinatorics 7, 177–181 (1991)
Molitor, P.: A survey on wiring. EIK Journal of Information Processing and Cybernetics 27, 3–19 (1991)
Sinden, F.: Topology of thin film circuits. Bell System Technical Journal 45, 1639–1662 (1966)
West, D.B.: Introduction to graph theory, 2nd edn. Prentice-Hall (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chaplick, S., Cohen, E., Stacho, J. (2011). Recognizing Some Subclasses of Vertex Intersection Graphs of 0-Bend Paths in a Grid. In: Kolman, P., Kratochvíl, J. (eds) Graph-Theoretic Concepts in Computer Science. WG 2011. Lecture Notes in Computer Science, vol 6986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25870-1_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-25870-1_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25869-5
Online ISBN: 978-3-642-25870-1
eBook Packages: Computer ScienceComputer Science (R0)