Abstract
Finding a minimum connected dominating set (connected domination) is known \(\cal{NP}\)-complete for chordal bipartite graphs, but tractable for convex bipartite graphs. In this paper, connected domination is shown tractable for circular- and triad-convex bipartite graphs, by efficient reductions from these graphs to convex bipartite graphs.
Partially supported by National 973 Program of China (Grant No. 2010CB328103).
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References
Damaschke, P., Müller, H., Kratsch, D.: Domination in Convex and Chordal Bipartite Graphs. Inf. Process. Lett. 36(5), 231–236 (1990)
Garey, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-Completeness. W.H. Freeman and Company (1979)
Grover, F.: Maximum matching in a convex bipartite graph. Nav. Res. Logist. Q. 14, 313–316 (1967)
Jiang, W., Liu, T., Ren, T., Xu, K.: Two Hardness Results on Feedback Vertex Sets. In: Atallah, M., Li, X.-Y., Zhu, B. (eds.) FAW-AAIM 2011. LNCS, vol. 6681, pp. 233–243. Springer, Heidelberg (2011)
Jiang, W., Liu, T., Wang, C., Xu, K.: Feedback vertex sets on restricted bipartite graphs. Theor. Comput. Sci. (in press, 2013), doi:10.1016/j.tcs.2012.12.021
Jiang, W., Liu, T., Xu, K.: Tractable Feedback Vertex Sets in Restricted Bipartite Graphs. In: Wang, W., Zhu, X., Du, D.-Z. (eds.) COCOA 2011. LNCS, vol. 6831, pp. 424–434. Springer, Heidelberg (2011)
Liang, Y.D., Blum, N.: Circular convex bipartite graphs: Maximum matching and Hamiltonian circuits. Inf. Process. Lett. 56, 215–219 (1995)
Müller, H., Brandstät, A.: The NP-completeness of steiner tree and dominating set for chordal bipartite graphs. Theor. Comput. Sci. 53(2-3), 257–265 (1987)
Pfaff, J., Laskar, R., Hedetniemi, S.T.: NP-completeness of total and connected domination, and irredundance for bipartite graphs. Technical Report 428, Dept. Mathematical Sciences, Clemenson Univ. (1983)
Sampathkumar, E., Walikar, H.B.: The connected domination number of a graph. Math. Phys. Sci. 13(6), 607–613 (1979)
Song, Y., Liu, T., Xu, K.: Independent Domination on Tree Convex Bipartite Graphs. In: Snoeyink, J., Lu, P., Su, K., Wang, L. (eds.) FAW-AAIM 2012. LNCS, vol. 7285, pp. 129–138. Springer, Heidelberg (2012)
Wang, C., Liu, T., Jiang, W., Xu, K.: Feedback vertex sets on tree convex bipartite graphs. In: Lin, G. (ed.) COCOA 2012. LNCS, vol. 7402, pp. 95–102. Springer, Heidelberg (2012)
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Lu, Z., Liu, T., Xu, K. (2013). Tractable Connected Domination for Restricted Bipartite Graphs (Extended Abstract). In: Du, DZ., Zhang, G. (eds) Computing and Combinatorics. COCOON 2013. Lecture Notes in Computer Science, vol 7936. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38768-5_65
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DOI: https://doi.org/10.1007/978-3-642-38768-5_65
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