Abstract
A 2-stab unit interval graph (2SUIG) is an axes-parallel unit square intersection graph where the unit squares intersect either of the two fixed lines parallel to the X-axis, distance \(1 + \epsilon \) (\(0< \epsilon < 1\)) apart. This family of graphs allow us to study local structures of unit square intersection graphs, that is, graphs with cubicity 2. The complexity of determining whether a tree has cubicity 2 is unknown while the graph recognition problem for unit square intersection graph is known to be NP-hard. We present a linear time algorithm for recognizing trees that admit a 2SUIG representation.
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References
Bhatt, S.N., Cosmadakis, S.S.: The complexity of minimizing wire lengths in VLSI layouts. Inf. Process. Lett. 25(4), 263–267 (1987)
Bhore, S.K., Chakraborty, D., Das, S., Sen, S.: On a special class of boxicity 2 graphs. In: Ganguly, S., Krishnamurti, R. (eds.) CALDAM 2015. LNCS, vol. 8959, pp. 157–168. Springer, Heidelberg (2015)
Breu, H.: Algorithmic aspects of constrained unit disk graphs. Ph.D. thesis, University of British Columbia (1996)
Clark, B.N., Colbourn, C.J., Johnson, D.S.: Unit disk graphs. Discrete Math. 86(1–3), 165–177 (1990)
Correa, J., Feuilloley, L., Pérez-Lantero, P., Soto, J.A.: Independent and hitting sets of rectangles intersecting a diagonal line: algorithms and complexity. Discrete Comput. Geom. 53(2), 344–365 (2015)
Imai, H., Asano, T.: Finding the connected components and a maximum clique of an intersection graph of rectangles in the plane. J. Algorithms 4(4), 310–323 (1983)
Babu, J., Basavaraju, M., Chandran, L.S., Rajendraprasad, D., Sivadasan, N.: Approximating the cubicity of trees. CoRR, abs/1402.6310 (2014)
KratochvÃl, J.: A special planar satisfiability problem and a consequence of its NP-completeness. Discrete Appl. Math. 52(3), 233–252 (1994)
Lekkeikerker, C., Boland, J.: Representation of a finite graph by a set of intervals on the real line. Fundamenta Math. 51(1), 45–64 (1962)
Roberts, F.S.: On the boxicity and cubicity of a graph. In: Recent Progresses in Combinatorics, pp. 301–310 (1969)
Scheinerman, E.R.: Characterizing intersection classes of graphs. Discrete Math. 55(2), 185–193 (1985)
West, D.B., Shmoys, D.B.: Recognizing graphs with fixed interval number is NP-complete. Discrete Appl. Math. 8(3), 295–305 (1984)
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Bhore, S., Chakraborty, D., Das, S., Sen, S. (2016). On Local Structures of Cubicity 2 Graphs. In: Chan, TH., Li, M., Wang, L. (eds) Combinatorial Optimization and Applications. COCOA 2016. Lecture Notes in Computer Science(), vol 10043. Springer, Cham. https://doi.org/10.1007/978-3-319-48749-6_19
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DOI: https://doi.org/10.1007/978-3-319-48749-6_19
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