Abstract
Fitch graphs G=(X,E) are di-graphs that are explained by {⊗,1}-edge-labeled rooted trees with leaf set X: there is an arc xy∈E if and only if the unique path in T that connects the least common ancestor 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 lca(x,y) to y.In this contribution, we generalize the concept of Fitch graphs and consider complete di-graphs K|X| with vertex set X and a map ε that assigns to each arc xy a unique label ε(x,y)∈M∪{⊗}, where M denotes an arbitrary set of symbols. A di-graph (K|X|,ε) is a generalized Fitch graph if there is an M∪{⊗}-edge-labeled tree (T,λ) that can explain (K|X|,ε).We provide a simple characterization of generalized Fitch graphs (K|X|,ε) 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|,ε).
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