Oriented bipartite graphs and the Goldbach graph

Das, Sandip; Ghosh, Prantar; Ghosh, Suparna; Sen, Sagnik

doi:10.1016/j.disc.2021.112497

Cited by 8 publications

(5 citation statements)

References 10 publications

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“…The main result of this section is Thm. 4, which shows that the support leaves of the root can be identified directly in the 2-BMG. In Sec.…”

Section: Introductionmentioning

confidence: 84%

“…Sink-free graphs have appeared in particular in the context of graph semigroups [1] and graph orientation problems [3]. Bi-transitive graphs were introduced in [4] in the context of oriented bipartite graphs and investigated in more detail in [7,8]. The class of graphs satisfying (N1), (N2), and (N3) are characterized by a system of forbidden induced subgraphs [12], see Thm.…”

Section: Introductionmentioning

confidence: 99%

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Least resolved trees for two-colored best match graphs

Schaller¹,

Geiß²,

Hellmuth³

et al. 2021

Preprint

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2-colored best match graphs (2-BMGs) form a subclass of sink-free bi-transitive graphs that appears in phylogenetic combinatorics. There, 2-BMGs describe evolutionarily most closely related genes between a pair of species. 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 approach can be extended to also recognize binary-explainable 2-BMGs with the same complexity. An empirical comparison emphasizes the efficiency of the new algorithm.

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“…The main result of this section is Thm. 4, which shows that the support leaves of the root can be identified directly in the 2-BMG. In Sec.…”

Section: Introductionmentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

Least resolved trees for two-colored best match graphs

Schaller¹,

Geiß²,

Hellmuth³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…A nice example of a bitransitive bitournament arises from arithmetic, see [5]. For a nonempty subset S of natural numbers, let Γ S (S, E) be the digraph with vertex set S such that uv ∈ E if u < v and u and v have opposite parity.…”

Section: Bitransitive Bitournamentsmentioning

confidence: 99%

“…It should be noticed however that N(1) and N(3) are properties which had not been considered at all in the literature on graph theory until the discovery of their links to evolutionary relatedness via phylogenetic trees whereas N(2), under the name of bitransitive property, was marginally studied in a recent manuscript [5] about bitournaments; see Section 4.…”

Section: Introductionmentioning

confidence: 99%

Circles and Paths in 2-Colored Best Match Graphs

Korchmaros

2020

Preprint

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Recent investigations in computational biology focus on a family of 2-colored digraphs, called 2-colored best match graphs, which naturally arise from rooted phylogenetic trees. Actually the defining properties of such graphs are unexpectedly unusual in graph theory, and they were established only recently after the discovery of their links to evolutionary relatedness via phylogenetic trees. In this paper several results are obtained on 2-colored best match graphs which well fit in the mainstream of graph theory.

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“…Every BMG therefore can be viewed as the disjoint union of (the arc sets of) 2-colored BMGs. These 2-BMGs [6,10,11] are bipartite and form a common subclass of the sink-free digraphs [1,2] and the bi-transitive digraphs [3].…”

Section: Introductionmentioning

confidence: 99%

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

Schaller¹,

Geiß²,

Hellmuth³

et al. 2021

Preprint

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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. BMGs are explained by unique least resolved trees. We prove that the property of a rooted, leaf-colored tree to be least resolved for some BMG is preserved by the contraction of inner edges. 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 completion of the arc set of a BMG to reach a BMG that can be explained by a binary tree.

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Oriented bipartite graphs and the Goldbach graph

Cited by 8 publications

References 10 publications

Least resolved trees for two-colored best match graphs

Least resolved trees for two-colored best match graphs

Circles and Paths in 2-Colored Best Match Graphs

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

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