Please use this identifier to cite or link to this item: https://doi.org/10.1007/s12190-012-0546-z
Title: The size of 3-compatible, weakly compatible split systems
Authors: Grünewald, S.
Koolen, J.H.
Moulton, V.
Wu, T. 
Keywords: Compatibility
Extremal combinatorics of finite sets
Phylogenetic combinatorics
Split systems
Weak compatibility
Issue Date: Oct-2012
Citation: Grünewald, S., Koolen, J.H., Moulton, V., Wu, T. (2012-10). The size of 3-compatible, weakly compatible split systems. Journal of Applied Mathematics and Computing 40 (1-2) : 249-259. ScholarBank@NUS Repository. https://doi.org/10.1007/s12190-012-0546-z
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. © 2012 Korean Society for Computational and Applied Mathematics.
Source Title: Journal of Applied Mathematics and Computing
URI: http://scholarbank.nus.edu.sg/handle/10635/104354
ISSN: 15985865
DOI: 10.1007/s12190-012-0546-z
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