相关论文: Characterizations of undirected 2-quasi best match…
Quasi-best match graphs (qBMGs) are a hereditary class of directed, properly vertex-colored graphs. They arise naturally in mathematical phylogenetics as a generalization of best match graphs, which formalize the notion of evolutionary…
The undirected underlying graph of a 2-quasi best match graph (2-qBMG) is proven not to contain any induced graph isomorphic to $P_6$ or $C_6$. This new feature allows for the investigation of 2-BMGs further by exploiting the numerous known…
2-quasi best match graphs (2-qBMGs) are directed graphs that capture a notion of close relatedness in phylogenetics. Here, we investigate the undirected underlying graph of a 2-qBMG (un-2qBMG) and show that they contain neither a path $P_l$…
2-colored quasi best match graphs (2-qBMGs) are directed graphs that arose in phylogenetics. Investigations of 2-qBMGs have mostly focused on computational issues. However, 2-qBMGs also have relevant properties for structural graph theory;…
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…
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…
Best match graphs (BMG) are a key intermediate in graph-based orthology detection and contain a large amount of information on the gene tree. We provide a near-cubic algorithm to determine whether a BMG is binary-explainable, i.e., whether…
Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs,…
A unit disk graph is the intersection graph of disks of equal radii in the plane. The class of unit disk graphs is hereditary, and therefore admits a characterization in terms of minimal forbidden induced subgraphs. In spite of quite active…
For any class $\mathcal{C}$ of bipartite graphs, we define quasi-$\cal C$ to be the class of all graphs $G$ such that every bipartition of $G$ belongs to $\cal C$. This definition is motivated by a generalisation of the switch Markov chain…
A simple undirected graph is said to be {\em semisymmetric} if it is regular and edge-transitive but not vertex-transitive. Every semisymmetric graph is a bipartite graph with two parts of equal size. It was proved in [{\em J. Combin.…
Recent investigations in computational biology have focused 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…
We study bipartite graphs partially ordered by the induced subgraph relation. Our goal is to distinguish classes of bipartite graphs which are or are not well-quasi-ordered (wqo) by this relation. Answering an open question from…
Best match graphs (BMGs) are vertex-colored directed graphs that were introduced to model the relationships of genes (vertices) from different species (colors) given an underlying evolutionary tree that is assumed to be unknown. In…
Let $G$ be a finite group. The bipartite divisor graph for the set of irreducible complex character degrees is the undirected graph with vertex set consisting of the prime numbers dividing some character degree and of the non-identity…
A biclique of a graph is a maximal complete bipartite subgraph. The biclique graph of a graph $G$, $KB(G)$, defined as the intersection graph of the bicliques of $G$, was introduced and characterized in 2010. However, this characterization…
Unigraphs are graphs identifiable up to isomorphism from their degree sequences. Given a class $\mathcal{A}$ of graphs, we define the class of $\mathcal{A}$-unigraphs to be graphs identifiable from degree sequence and membership in…
Reciprocal best matches play an important role in numerous applications in computational biology, in particular as the basis of many widely used tools for orthology assessment. Nevertheless, very little is known about their mathematical…
In this paper, we study oriented bipartite graphs. In particular, we introduce "bitransitive" graphs. Several characterizations of bitransitive bitournaments are obtained. We show that bitransitive bitounaments are equivalent to acyclic…
The mirror (or bipartite complement) mir(B) of a bipartite graph B=(X,Y,E) has the same color classes X and Y as B, and two vertices x in X and y in Y are adjacent in mir(B) if and only if xy is not in E. A bipartite graph is chordal…