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The size of 3-compatible, weakly compatible split systems

  • Applicable mathematics in biological
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Abstract

A split system on a finite set X is a set of bipartitions of X. Weakly compatible and k-compatible (k≥1) split systems are split systems which satisfy special restrictions on all subsets of a certain fixed size. They arise in various areas of applied mathematics such as phylogenetics and multi-commodity flow theory. In this note, we show that the number of splits in a 3-compatible, weakly compatible split system on a set X of size n is linear in n.

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Acknowledgements

TW and VM were supported by the Engineering and Physical Sciences Research Council [grant number EP/D068800/1]. VM thanks the Royal Society for enabling him to visit TW and JK in Singapore. TW was also partially supported by the Singapore MOE grant R-146-000-134-112. JK was partially supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (grant number 2010-0008138).

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Authors and Affiliations

  1. CAS-MPG Partner Institute for Computational Biology (PICB), Key Laboratory of Computational Biology, Shanghai Institutes for Biological Sciences, 320 Yue Yang Road, Shanghai, 200031, P.R. China

    Stefan Grünewald

  2. Department of Mathematics, POSTECH, Pohang, 790-784, South Korea

    Jack H. Koolen

  3. School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ, UK

    Vincent Moulton & Taoyang Wu

  4. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge, Singapore, 119076, Singapore

    Taoyang Wu

Authors
  1. Stefan Grünewald
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  2. Jack H. Koolen
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  3. Vincent Moulton
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  4. Taoyang Wu
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Correspondence to Taoyang Wu.

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Grünewald, S., Koolen, J.H., Moulton, V. et al. The size of 3-compatible, weakly compatible split systems. J. Appl. Math. Comput. 40, 249–259 (2012). https://doi.org/10.1007/s12190-012-0546-z

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  • DOI: https://doi.org/10.1007/s12190-012-0546-z

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