Abstract
In this paper we consider the problem of finding minimum independent edge dominating sets in graphs of maximum degree three. The problem is NP-hard. We present an algorithm which finds the dominating set of size at most 4n/9+1/3. Using this bound we achieve an approximation ratio of 40/27 for the minimum independent edge domination set problem in cubic graphs.
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Chlebík, M., Chlebíková, J.: Approximation Hardness of Minimum Edge Dominating Set and Minimum Maximal Matching. In: Ibaraki, T., Katoh, N., Ono, H. (eds.) ISAAC 2003. LNCS, vol. 2906, pp. 415–424. Springer, Heidelberg (2003)
Duckworth, W., Wormald, N.C.: Linear Programming and the Worst-Case Analysis of Greedy Algorithms on Cubic Graphs (unpublished)
Horton, J.D., Kilakos, K.: Minimum Edge Dominating Sets. SIAM Journal on Discrete Mathematics 6(3), 375–387 (1993)
Loryś, K., Zwoźniak, G.: Approximation Algorithm for the Maximum Leaf Spanning Tree Problem for Cubic Graphs. In: Möhring, R.H., Raman, R. (eds.) ESA 2002. LNCS, vol. 2461, pp. 686–697. Springer, Heidelberg (2002)
Yannakakis, M., Gavril, F.: Edge Dominating Sets in Cubic Graphs. SIAM Journal on Applied Mathematics 38(3), 364–372 (1980)
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© 2006 Springer-Verlag Berlin Heidelberg
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Zwoźniak, G. (2006). Small Independent Edge Dominating Sets in Graphs of Maximum Degree Three. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds) SOFSEM 2006: Theory and Practice of Computer Science. SOFSEM 2006. Lecture Notes in Computer Science, vol 3831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11611257_54
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DOI: https://doi.org/10.1007/11611257_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-31198-0
Online ISBN: 978-3-540-32217-7
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