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On a Conjecture about Compatibility of Multi-states Characters

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Algorithms in Bioinformatics (WABI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 6833))

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Abstract

Perfect phylogeny consisting of determining the compatibility of a set of characters is known to be NP-complete [4,28]. We propose in this article a conjecture on the necessary and sufficient conditions of compatibility: Given a set \(\mathcal{C}\) of r-states full characters, there exists a function f(r) such that \(\mathcal{C}\) is compatible iff every set of f(r) characters of \(\mathcal{C}\) is compatible. According to [7,9,8,25,11,23], f(2) = 2, f(3) = 3 and f(r) ≥ r. [23] conjectured that f(r) = r for any r ≥ 2. In this paper, we present an example showing that f(4) ≥ 5. Therefore it could be the case that for r ≥ 4 characters the problem behavior drastically changes. In a second part, we propose a closure operation for chordal sandwich graphs. The later problem is a common approach of perfect phylogeny.

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Authors and Affiliations

  1. Université Paris Diderot - Paris 7, LIAFA, Case 701, 75205, Paris Cedex 13, France

    Michel Habib & Thu-Hien To

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  1. Michel Habib
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  2. Thu-Hien To
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Editors and Affiliations

  1. National Center for Biotechnology Information, U.S. National Library of Medicine, 8600 Rockville Pike, 20894, Bethesda, MD, USA

    Teresa M. Przytycka

  2. Institut National de Recherche en Informatique et en Automatique (INRIA) and Université Lyon 1 (UCBL), 43 bd du 11 Novembre 1918, 69622, Villeurbanne cedex, France

    Marie-France Sagot

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Habib, M., To, TH. (2011). On a Conjecture about Compatibility of Multi-states Characters. In: Przytycka, T.M., Sagot, MF. (eds) Algorithms in Bioinformatics. WABI 2011. Lecture Notes in Computer Science(), vol 6833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23038-7_11

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  • DOI: https://doi.org/10.1007/978-3-642-23038-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23037-0

  • Online ISBN: 978-3-642-23038-7

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