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- W2785602753 abstract "Fitch graphs $G=(X,E)$ are di-graphs that are explained by ${otimes,1}$-edge-labeled rooted trees with leaf set $X$: there is an arc $xyin E$ if and only if the unique path in $T$ that connects the least common ancestor $textrm{lca}(x,y)$ of $x$ and $y$ with $y$ contains at least one edge with label $1$. In practice, Fitch graphs represent xenology relations, i.e., pairs of genes $x$ and $y$ for which a horizontal gene transfer happened along the path from $textrm{lca}(x,y)$ to $y$. In this contribution, we generalize the concept of xenology and Fitch graphs and consider complete di-graphs $K_{|X|}$ with vertex set $X$ and a map $epsilon$ that assigns to each arc $xy$ a unique label $epsilon(x,y)in Mcup {otimes}$, where $M$ denotes an arbitrary set of symbols. A di-graph $(K_{|X|},epsilon)$ is a generalized Fitch graph if there is an $Mcup {otimes}$-edge-labeled tree $(T,lambda)$ that can explain $(K_{|X|},epsilon)$. We provide a simple characterization of generalized Fitch graphs $(K_{|X|},epsilon)$ and give an $O(|X|^2)$-time algorithm for their recognition as well as for the reconstruction of the unique least resolved phylogenetic tree that explains $(K_{|X|},epsilon)$." @default.
- W2785602753 created "2018-02-23" @default.
- W2785602753 creator A5019719296 @default.
- W2785602753 date "2018-02-10" @default.
- W2785602753 modified "2023-09-27" @default.
- W2785602753 title "Generalized Fitch Graphs: Edge-labeled Graphs that are explained by Edge-labeled Trees" @default.
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- W2785602753 hasPublicationYear "2018" @default.
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