scholarly journals Finding a Longest Path in a Complete Multipartite Digraph

1993 ◽  
Vol 6 (2) ◽  
pp. 270-273 ◽  
Author(s):  
G. Gutin
Keyword(s):  
Longest Path ◽  
Complete Multipartite

A Nettree for Simple Paths with Length Constraint and the Longest Path in Directed Acyclic Graphs

2012 ◽  
Vol 35 (10) ◽  
pp. 2194 ◽  
Author(s):  
Yan LI ◽  
Le SUN ◽  
Huai-Zhong ZHU ◽  
You-Xi WU
Keyword(s):  
Directed Acyclic Graphs ◽  
Length Constraint ◽  
Acyclic Graphs ◽  
Longest Path ◽  
Simple Paths

scholarly journals Indirect identification of horizontal gene transfer

2021 ◽  
Vol 83 (1) ◽  
Author(s):  
David Schaller ◽  
Manuel Lafond ◽  
Peter F. Stadler ◽  
Nicolas Wieseke ◽  
Marc Hellmuth
Keyword(s):  
Gene Transfer ◽  
Horizontal Gene Transfer ◽  
Polynomial Time ◽  
Divergence Time ◽  
Recognition Algorithm ◽  
Vertex Coloring ◽  
Implicit Methods ◽  
Colored Graphs ◽  
Wide Range ◽  
Complete Multipartite

AbstractSeveral 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 later-divergence-time (LDT) graph, whose vertices correspond to genes colored by their species. We investigate these graphs in the setting of relaxed scenarios, i.e., evolutionary scenarios that encompass all commonly used variants of duplication-transfer-loss scenarios in the literature. We characterize LDT graphs as a subclass of properly vertex-colored cographs, and provide a polynomial-time recognition algorithm as well as an algorithm to construct a relaxed 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 converse is not true, however. We show that the complete xenology relation is described by an rs-Fitch graph, i.e., a complete multipartite graph satisfying constraints on the vertex coloring. This class of vertex-colored 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.

scholarly journals A linear-time algorithm for the longest path problem in rectangular grid graphs

2012 ◽  
Vol 160 (3) ◽  
pp. 210-217 ◽  
Author(s):  
Fatemeh Keshavarz-Kohjerdi ◽  
Alireza Bagheri ◽  
Asghar Asgharian-Sardroud
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Rectangular Grid ◽  
Grid Graphs ◽  
Longest Path ◽  
Longest Path Problem
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