
Explicit 3colorings for exponential graphs
Let H=(V,E) denote a simple, undirected graph. The 3coloring exponentia...
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Algorithms for the rainbow vertex coloring problem on graph classes
Given a vertexcolored graph, we say a path is a rainbow vertex path if ...
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Best Match Graphs and Reconciliation of Gene Trees with Species Trees
A wide variety of problems in computational biology, most notably the as...
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Listthreecoloring P_tfree graphs with no induced 1subdivision of K_1,s
Let s and t be positive integers. We use P_t to denote the path with t v...
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Incompressibility of Hfree edge modification problems: Towards a dichotomy
Given a graph G and an integer k, the Hfree Edge Editing problem is to ...
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Reconstructing Gene Trees From Fitch's Xenology Relation
Two genes are xenologs in the sense of Fitch if they are separated by at...
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Partial Orthology, Paralogy and Xenology Relations  Satisfiability in terms of DiCographs
A variety of methods based on sequence similarity, reconciliation, synte...
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Indirect Identification of Horizontal Gene Transfer
Several implicit methods to infer Horizontal Gene Transfer (HGT) focus on pairs of genes that have diverged only after the divergence of the two species in which the genes reside. This situation defines the edge set of a graph, the laterdivergencetime (LDT) graph, whose vertices correspond to genes colored by their species. We investigate these graphs in the setting of relaxed evolutionary scenarios that encompass all commonly used variants of duplicationtransferloss scenarios in the literature. We characterize LDT graphs as a subclass of properly vertexcolored cographs, and provide a polynomialtime recognition algorithm as well as an algorithm to construct an evolutionary scenario that explains a given LDT. An edge in an LDT graph implies that the two corresponding genes are separated by at least one HGT event. The conserve is not true, however. We show that the complete xenology relation is described by an rsFitch graph, i.e., a complete multipartite graph satisfying constraints on the vertex coloring. This class of vertexcolored graphs is also recognizable in polynomial time. We finally address the question "how much information about all HGT events is contained in LDT graphs" with the help of simulations of evolutionary scenarios with a wide range of duplication, loss, and HGT events. In particular, we show that a simple greedy graph editing scheme can be used to efficiently detect HGT events that are implicitly contained in LDT graphs.
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