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Kernelization for Cycle Transversal Problems

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Algorithmic Aspects in Information and Management (AAIM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6124))

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Abstract

We present new kernelization results for the s -cycle transversal problem for s > 3. In particular, we show a 6k 2 kernel for 4-cycle transversal and a O(k s − 1) kernel for s -cycle transversal when s > 4. We prove the NP-completeness of s -cycle transversal on planar graphs and obtain a 74k kernel for 4-cycle transversal on planar graphs. We also give several kernelization results for a related problem ( ≤ s)-cycle transversal.

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References

  1. Abu-Khzam, F.N.: Kernelization algorithms for d-hitting set problems. In: WADS, pp. 434–445 (2007)

    Google Scholar 

  2. Alon, N.: Bipartite subgraphs. Combinatorica 16, 301–311 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bodlaender, H.L., Fomin, F.V., Lokshtanov, D., Penninkx, E., Saurabh, S., Thilikos, D.M.: (meta) kernelization. In: Proceedings of the 50th Annual IEEE Symposium on Foundations of Computer Science (2009)

    Google Scholar 

  4. Borodin, O.V., Kostochka, A.V., Sheikh, N.N., Yu, G.: M-degrees of quadrangle-free planar graphs. J. Graph Theory 60(1), 80–85 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Brügmann, D., Komusiewicz, C., Moser, H.: On generating triangle-free graphs. Electronic Notes in Discrete Mathematics 32, 51–58 (2009)

    Article  Google Scholar 

  6. Cherlin, G., Komjáth, P.: There is no universal countable pentagon-free graph. J. Graph Theory 18(4), 337–341 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  7. Downey, R., Fellows, M.: Parameterized Complexity. Springer, Heidelberg (1999)

    Google Scholar 

  8. Esperet, L., Montassier, M., Zhu, X.: Adapted list coloring of planar graphs. J. Graph Theory 62(2), 127–138 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  9. Fernau, H.: Speeding up exact algorithms with high probability. Electronic Notes in Discrete Mathematics 25, 57–59 (2006)

    Article  MathSciNet  Google Scholar 

  10. Füredi, Z.: On the number of edges of quadrilateral-free graphs. J. Comb. Theory Ser. B 68(1), 1–6 (1996)

    Article  MATH  Google Scholar 

  11. Füredi, Z., Naor, A., Verstraete, J.: On the turan number for the hexagon. Advances in Mathematics 203(2), 476–496 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Guo, J., Niedermeier, R.: Invitation to data reduction and problem kernelization. SIGACT News 38(1), 31–45 (2007)

    Article  Google Scholar 

  13. Guo, J., Niedermeier, R.: Linear problem kernels for NP-hard problems on planar graphs. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 375–386. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Györi, E., Lemons, N.: Hypergraphs with no odd cycle of given length. Electronic Notes in Discrete Mathematics 34, 359–362 (2009)

    Article  Google Scholar 

  15. Halford, T.R., Grant, A.J., Chugg, K.M.: Which codes have 4-cycle-free tanner graphs? IEEE Transactions on Information Theory 52(9), 4219–4223 (2006)

    Article  MathSciNet  Google Scholar 

  16. Khot, S., Regev, O.: Vertex cover might be hard to approximate to within 2-epsilon. J. Comput. Syst. Sci. 74(3), 335–349 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  17. Kortsarz, G., Langberg, M., Nutov, Z.: Approximating maximum subgraphs without short cycles. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds.) APPROX and RANDOM 2008. LNCS, vol. 5171, pp. 118–131. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  18. Krivelevich, M.: On a conjecture of tuza about packing and covering of triangles. Discrete Math. 142(1-3), 281–286 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  19. Veni Madhavan, C.E.: Foundations of Software Technology and Theoretical Computer Science, vol. 181, pp. 381–392. Springer, Heidelberg (1984)

    Google Scholar 

  20. Moser, H.: A problem kernelization for graph packing. In: Nielsen, M., Kucera, A., Miltersen, P.B., Palamidessi, C., Tuma, P., Valencia, F.D. (eds.) SOFSEM 2009. LNCS, vol. 5404, pp. 401–412. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  21. Naor, A., Verstraëte, J.: A note on bipartite graphs without 2k-cycles. Comb. Probab. Comput. 14(5-6), 845–849 (2005)

    Article  MATH  Google Scholar 

  22. Thomassen, C.: On the chromatic number of triangle-free graphs of large minimum degree. Combinatorica 22(4), 591–596 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  23. Thomassen, C.: On the chromatic number of pentagon-free graphs of large minimum degree. Combinatorica 27(2), 241–243 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  24. Yannakakis, M.: Node-and edge-deletion NP-complete problems. In: STOC, pp. 253–264 (1978)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, Lafayette College, Easton, PA, 18042

    Ge Xia

  2. Department of Computer Science, Kutztown University, Kutztown, PA, 19530

    Yong Zhang

Authors
  1. Ge Xia
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  2. Yong Zhang
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Editor information

Editors and Affiliations

  1. Warwick Business School/ DIMAP - Centre for Discrete Mathematics and its Applications Coventry, University of Warwick, CV4 7AL, UK

    Bo Chen

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Xia, G., Zhang, Y. (2010). Kernelization for Cycle Transversal Problems. In: Chen, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2010. Lecture Notes in Computer Science, vol 6124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14355-7_30

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  • DOI: https://doi.org/10.1007/978-3-642-14355-7_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14354-0

  • Online ISBN: 978-3-642-14355-7

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