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Radosław Ziemann



Authors and WSEAS

Radosław Ziemann


WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 18, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 18, 2019



A Linear Algorithm for Connected Domination in Partial k-Trees

AUTHORS: Radosław Ziemann

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: In this paper we claim that the Corollary 2 in [V. Pinciu, Dominating sets for outerplanar graphs, WSEAS Transactions on Mathematics 1(3), 2004, pp. 55–58] is false. In particular, we present a linear-time algorithm for partial k-trees that solves the problem.

KEYWORDS: Algorithm, connected domination, linear-time, partial k-trees

REFERENCES:

[ 1] R. E. Bellman, S. E. Dreyfus, Applied Dynamic Programming, Princeton University Press, 1962.

[2] H. L. Bodlaender, A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM J. Comput. 25(6), 1996. pp. 1305-1317.

[3] H. L. Bodlaender, Dynamic programming on graphs with bounded treewidth, International Colloquium on Automata, Languages, and Programming, 1988, pp. 105–118.

[4] B. Courcelle, The monadic second-order logic of graphs. I. Recognizable sets of finite graphs, Inf. Comput. 85(1), 1990, pp. 12–75.

[5] W. J. Desormeaux, T. W. Haynes, M. A. Henning, Bounds on the connected domination number of a graph, Discrete Appl. Math. 161(18), 2013, pp. 2925–2931.

[6] R. Diestel, Graph Theory, Springer, Heidelberg, 2012.

[7] W. Duckworth, B. Mansb, Connected domination of regular graphs, Discrete Math. 309(8), 2009, pp. 2305–2322.

[8] M. Frick, M. Grohe, The complexity of firstorder and monadic second-order logic revisited, Ann. Pure Appl. Logic 130(13), 2004, pp. 3–31.

[9] H. Karami, A. Khodkar, S. M. Sheikholeslami, D. B. West, Connected domination number of a graph and its complement, Graphs Combin. 28(1), 2012, pp. 123–131.

[10] M. Lema ´nska, E. Rivera-Campo, R. Ziemann, R. Zuazua, P. Zyli ´nski, Convex dominating sets ˙ in maximal outerplanar Graphs, Discrete Appl. Math. 265, 2019, pp. 142–157.

[11] V. Pinciu, Dominating sets for outerplanar graphs, WSEAS Transactions on Mathematics 1(3), 2004, pp. 55–58.

[12] D. Rose, G. Lueker, R. E. Tarjan, Algorithmic aspects of vertex elimination on graphs. SIAM J. Comput. 5(2), 1976, pp. 266–283.

[13] N. Robertson, P. D. Seymour, Graph minors. II. Algorithmic aspects of treewidth, J. Algorithms 7, 1986, pp. 309–322.

[14] E. Sampathkumar, H. B. Walikar, The connected domination number of a graph, J. Math. Phys. Sci. 13(6), 1979, pp. 607–613.

[15] M. Sysło, Characterizations of outerplanar graphs, Discrete Math. 26(1), 1979, pp. 47–53.

[16] J. A. Telle, A. Proskurowski, Practical algorithms on partial k-trees with an application to domination-like problems, Workshop on Algorithms and Data Structures, 1993, pp. 610–621.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 18, 2019, Art. #32, pp. 237-240


Copyright Β© 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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