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Least resolved trees for two-colored best match graphs [article]

David Schaller, Manuela Geiß, Marc Hellmuth, Peter F. Stadler
2021 arXiv   pre-print
2-colored best match graphs (2-BMGs) form a subclass of sink-free bi-transitive graphs that appears in phylogenetic combinatorics.  ...  They are explained by a unique least resolved tree (LRT). Introducing the concept of support vertices we derive an O(|V|+|E|log^2|V|)-time algorithm to recognize 2-BMGs and to construct its LRT.  ...  The best matches between genes of two species form a bipartite directed graph, the 2-colored best match graph or 2-BMG, that is determined by the phylogenetic tree describing the evolution of the genes  ... 
arXiv:2101.07000v1 fatcat:s453meujmngzrmkhxojsbccdfu

Best Match Graphs [article]

Manuela Geiß, Edgar Chavez, Marcos Gonzalez, Alitzel Lopez, Bärbel M. R. Stadler, Dulce I. Valdivia, Marc Hellmuth, Maribel H. Rosales,, Peter F. Stadler
2018 arXiv   pre-print
Best match graphs arise naturally as the first processing intermediate in algorithms for orthology detection. Let T be a phylogenetic (gene) tree T and σ an assignment of leaves of T to species.  ...  If the answer is affirmative, there is a unique least resolved tree that explains (G,σ), which can also be constructed in cubic time.  ...  Asymptotically, the approach via informative triples, Alg. 3, is therefore at best as good as the direct construction of the least resolved tree T * (H ) with Alg. 2. Effort in the n-color case.  ... 
arXiv:1803.10989v3 fatcat:htijdx76lvb5lbtqifjre5qiaq

Arc-Completion of 2-Colored Best Match Graphs to Binary-Explainable Best Match Graphs

David Schaller, Manuela Geiß, Marc Hellmuth, Peter F. Stadler
2021 Algorithms  
For the special case of two-colored BMGs, this leads to a characterization of the least resolved trees (LRTs) of binary-explainable trees and a simple, polynomial-time algorithm for the minimum cardinality  ...  Best match graphs (BMGs) are vertex-colored digraphs that naturally arise in mathematical phylogenetics to formalize the notion of evolutionary closest genes w.r.t. an a priori unknown phylogenetic tree  ...  Best Match Graphs, Least Resolved Trees, and Binary-Explainable BMGs In this section, we first summarize some properties of best match graphs and their least resolved trees.  ... 
doi:10.3390/a14040110 fatcat:oq4njhqwgbdwhaf7cfomebimiy

Arc-Completion of 2-Colored Best Match Graphs to Binary-Explainable Best Match Graphs [article]

David Schaller, Manuela Geiß, Marc Hellmuth, Peter F. Stadler
2021 arXiv   pre-print
For the special case of two-colored BMGs, this leads to a characterization of the least resolved trees (LRTs) of binary-explainable trees and a simple, polynomial-time algorithm for the minimum cardinality  ...  Best match graphs (BMGs) are vertex-colored digraphs that naturally arise in mathematical phylogenetics to formalize the notion of evolutionary closest genes w.r.t. an a priori unknown phylogenetic tree  ...  Best Match Graphs, Least Resolved Trees, and Binary-Explainable BMGs In this section, we first summarize some properties of best match graphs and their least resolved trees.  ... 
arXiv:2103.06665v1 fatcat:oxm3sluvcbdsbjwk3b32g4wbpa

Best match graphs

Manuela Geiß, Edgar Chávez, Marcos González Laffitte, Alitzel López Sánchez, Bärbel M. R. Stadler, Dulce I. Valdivia, Marc Hellmuth, Maribel Hernández Rosales, Peter F. Stadler
2019 Journal of Mathematical Biology  
Best match graphs arise naturally as the first processing intermediate in algorithms for orthology detection.  ...  If the answer is affirmative, there is a unique least resolved tree that explains [Formula: see text], which can also be constructed in cubic time.  ...  is is a colored best match graph.  ... 
doi:10.1007/s00285-019-01332-9 pmid:30968198 pmcid:PMC6534531 fatcat:nsiwxfrxpzcxncjenndfnvpv44

Best Match Graphs with Binary Trees [article]

David Schaller, Manuela Geiß, Marc Hellmuth, Peter F. Stadler
2021 arXiv   pre-print
Best match graphs (BMG) are a key intermediate in graph-based orthology detection and contain a large amount of information on the gene tree.  ...  Moreover, we show that all such binary trees are refinements of the unique binary-resolvable tree (BRT), which in general is a substantial refinement of the also unique least resolved tree of a BMG.  ...  (C) The best match graph (G, σ) explained by (T, σ). (D) The unique least resolved tree (T * , σ) explaining (G, σ).  ... 
arXiv:2011.00511v2 fatcat:7gkl3b3m6vcrxofkifrw7zk4fa

Corrigendum to "Best match graphs"

David Schaller, Manuela Geiß, Edgar Chávez, Marcos González Laffitte, Alitzel López Sánchez, Bärbel M. R. Stadler, Dulce I. Valdivia, Marc Hellmuth, Maribel Hernández Rosales, Peter F. Stadler
2021 Journal of Mathematical Biology  
The amended results simplify the construction of least resolved trees for n-cBMGs, i.e., Algorithm 1. All other results remain unchanged and are correct as stated.  ...  AbstractTwo errors in the article Best Match Graphs (Geiß et al. in JMB 78: 2015–2057, 2019) are corrected.  ...  Moreover, there must be a least resolved tree (T * , σ ) for (G, σ ).  ... 
doi:10.1007/s00285-021-01601-6 pmid:33818665 fatcat:q3aciozqxbhu5h75qcv3sgijbu

Complete Characterization of Incorrect Orthology Assignments in Best Match Graphs [article]

David Schaller, Manuela Geiß, Peter F. Stadler, Marc Hellmuth
2020 arXiv   pre-print
We consider duplication/loss scenarios and characterize unambiguous false-positive (u-fp) orthology assignments, that is, edges in the best match graphs (BMGs) that cannot correspond to orthologs for any  ...  Incorrect orthology assignments therefore are always false positives in the reciprocal best match graph.  ...  Seemann for fruitful discussions and his helpful  ... 
arXiv:2006.02249v2 fatcat:qlukurxl2bb3vlw5je7sykkr3m

Quasi-Best Match Graphs [article]

Annachiara Korchmaros, David Schaller, Marc Hellmuth, Peter F. Stadler
2021 arXiv   pre-print
Quasi-best match graphs (qBMGs) are a hereditary class of directed, properly vertex-colored graphs.  ...  They are explained by rooted trees whose leaves correspond to vertices. In contrast to BMGs, qBMGs represent only best matches at a restricted phylogenetic distance.  ...  Quasi-best match graphs that can be explained by a tree (T, σ, u) satisfying (M) are also of interest for more than two colors.  ... 
arXiv:2109.10235v1 fatcat:fmpzmadhfff4hbq4q4tvkulxse

Complete Characterization of Incorrect Orthology Assignments in Best Match Graphs

David Schaller, Manuela Geiß, Peter F Stadler, Marc Hellmuth
2021 Journal of Mathematical Biology  
We consider duplication/loss scenarios and characterize unambiguous false-positive (u-fp) orthology assignments, that is, edges in the best match graphs (BMGs) that cannot correspond to orthologs for any  ...  Incorrect orthology assignments therefore are always false positives in the reciprocal best match graph.  ...  Seemann for fruitful discussions and his helpful comments.  ... 
doi:10.1007/s00285-021-01564-8 pmid:33606106 pmcid:PMC7894253 fatcat:oox4eoaqxvezjktmgsihq63aay

Page 8084 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
for matching forests.  ...  Suppose that for a fixed integer k and a small ¢ > 0, a graph G on n vertices is such that at least en? edges should be deleted to make it k-colorable.  ... 

Heuristic algorithms for best match graph editing

David Schaller, Manuela Geiß, Marc Hellmuth, Peter F. Stadler
2021 Algorithms for Molecular Biology  
The corresponding graph editing problem can be used to guide error correction for best match data.  ...  Background Best match graphs (BMGs) are a class of colored digraphs that naturally appear in mathematical phylogenetics as a representation of the pairwise most closely related genes among multiple species  ...  Acknowledgements We thank the anonymous referees for their helpful comments.  ... 
doi:10.1186/s13015-021-00196-3 fatcat:tvkwfqoc2facbioatyd366pbpe

Reciprocal Best Match Graphs [article]

Manuela Geiß and Peter F. Stadler and Marc Hellmuth
2019 arXiv   pre-print
The (least resolved) trees that explain co-RBMGs can be constructed in polynomial time.  ...  Here, we investigate the structure of reciprocal best match graphs (RBMGs).  ...  so called least resolved tree.  ... 
arXiv:1903.07920v5 fatcat:n7kgpeajyrhordcl2bh2izvlei

Page 5168 of Mathematical Reviews Vol. , Issue 2004g [page]

2004 Mathematical Reviews  
This extends the well-known theorem of Gallai, that a k-color-critical graph with a connected complement has at least 2k — 1 vertices. The proof does not use matching theory.  ...  Summary: “It is known that if every vertex v of an outerplanar graph G is given a list L(v) of at least two colours, then G has an (L,2)*-coloring; that is, one can colour each vertex with a colour from  ... 

Best Match Graphs and Reconciliation of Gene Trees with Species Trees [article]

Manuela Geiß, Marcos E. González, Alitzel López Sánchez, Dulce I. Valdivia, Marc Hellmuth, Maribel Hernández Rosales, Peter F. Stadler
2019 arXiv   pre-print
We show that the orthology graph is a subgraph of the reciprocal best match graph (RBMG).  ...  Using an evolutionary definition of best matches that captures the intuition behind the concept we clarify rigorously the relationships between reciprocal best matches, orthology, and evolutionary events  ...  A Extraction of Graphs from Simulated Evolutionary Scenarios The simulations of evolutionary scenarios (described in the main text) result in an event-labeled gene tree (T,t, σ ) as well as an explicit  ... 
arXiv:1904.12021v3 fatcat:kh3b2haijjajlap6etgilc7qke
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