Abstract
Conflict free q-Colouring of a graph G refers to the colouring of a subset of vertices of G using q colours such that every vertex has a neighbour of unique colour. In this paper, we study the Minimum Conflict free q-Colouring problem. Given a graph G and a fixed constant q, Minimum Conflict free q-Colouring is to find a Conflict free q-Colouring of G that minimises the number of coloured vertices. We study the Minimum Conflict free q-Colouring problem parameterized by the treewidth of G. We give an FPT algorithm for this problem and also prove running time lower bounds under Exponential Time Hypothesis (ETH) and Strong Exponential Time Hypothesis (SETH).
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References
Abel, Z., et al.: Conflict-free coloring of graphs. SIAM J. Discrete Math. 32(4), 2675–2702 (2018)
Bodlaender, H.L., Kolay, S., Pieterse, A.: Parameterized complexity of conflict-free graph coloring. In: Algorithms and Data Structures - 16th International Symposium, WADS 2019, Edmonton, AB, Canada, 5–7 August 2019, Proceedings, pp. 168–180 (2019). https://doi.org/10.1007/978-3-030-24766-9_13
Courcelle, B.: The monadic second-order logic of graphs. I. Recognizable sets of finite graphs. Inf. Comput. 85(1), 12–75 (1990)
Cygan, M., et al.: Parameterized Algorithms, vol. 4. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21275-3
Downey, R.G., Fellows, M.R.: Parameterized Complexity. Springer, Switzerland (2012). https://doi.org/10.1007/978-3-319-21275-3
Even, G., Lotker, Z., Ron, D., Smorodinsky, S.: Conflict-free colorings of simple geometric regions with applications to frequency assignment in cellular networks. SIAM J. Comput. 33(1), 94–136 (2003)
Kratochvíl, J., Křivánek, M.: On the computational complexity of codes in graphs. In: Chytil, M.P., Koubek, V., Janiga, L. (eds.) MFCS 1988. LNCS, vol. 324, pp. 396–404. Springer, Heidelberg (1988). https://doi.org/10.1007/BFb0017162
Lokshtanov, D., Marx, D., Saurabh, S.: Known algorithms on graphs of bounded treewidth are probably optimal. In: Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 777–789. SIAM (2011)
Muzi, I., O’Brien, M.P., Reidl, F., Sullivan, B.D.: Being even slightly shallow makes life hard. In: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017), vol. 83, p. 79. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik (2017)
Pach, J., Tardos, G.: Conflict-free colourings of graphs and hypergraphs. Comb. Probab. Comput. 18(5), 819–834 (2009)
Schaefer, T.J.: The complexity of satisfiability problems. In: Proceedings of the Tenth Annual ACM Symposium on Theory of Computing, pp. 216–226. ACM (1978)
Yen, C.C., Lee, R.C.T.: The weighted perfect domination problem. Inf. Process. Lett. 35(6), 295–299 (1990)
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Ashok, P., Bhargava, R., Gupta, N., Khalid, M., Yadav, D. (2020). Minimum Conflict Free Colouring Parameterized by Treewidth. In: Changat, M., Das, S. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2020. Lecture Notes in Computer Science(), vol 12016. Springer, Cham. https://doi.org/10.1007/978-3-030-39219-2_35
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DOI: https://doi.org/10.1007/978-3-030-39219-2_35
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