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- W2950202301 abstract "Perfect phylogeny consisting of determining the compatibility of a set of characters is known to be NP-complete. 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. Some previous work showed that $f(2)=2$, $f(3)=3$ and $f(r) ge r-1$. Gusfield et al. 09 conjectured that $f(r) = r$ for any $r ge 2$. In this paper, we present an example showing that $f(4) ge 5$ and then a closure operation for chordal sandwich graphs. The later problem is a common approach of perfect phylogeny. This operation can be the first step to simplify the problem before solving some particular cases $f(4), f(5), ... $, and determining the function $f(r)$." @default.
- W2950202301 created "2019-06-27" @default.
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- W2950202301 date "2011-05-05" @default.
- W2950202301 modified "2023-10-16" @default.
- W2950202301 title "On a conjecture of compatibility of multi-states characters" @default.
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