Related papers: Unique Perfect Phylogeny Characterizations via Uni…
We introduce a novel representation of structured polynomial ideals, which we refer to as chordal networks. The sparsity structure of a polynomial system is often described by a graph that captures the interactions among the variables.…
A multifamily set representation of a finite simple graph $G$ is a multifamily $\mathcal{F}$ of sets (not necessarily distinct) for which each set represents a vertex in $G$ and two sets in $\mathcal{F}$ intersects if and only if the two…
Graph partitioning is a key fundamental problem in the area of big graph computation. Previous works do not consider the practical requirements when optimizing the big data analysis in real applications. In this paper, motivated by…
Graph matching problem aims to identify node correspondence between two or more correlated graphs. Previous studies have primarily focused on models where only edge information is provided. However, in many social networks, not only the…
The geometric dual of a cellularly embedded graph is a fundamental concept in graph theory and also appears in many other branches of mathematics. The partial dual is an essential generalization which can be obtained by forming the…
Graph packing and partitioning problems have been studied in many contexts, including from the algorithmic complexity perspective. Consider the packing problem of determining whether a graph contains a spanning tree and a cycle that do not…
The benefits of a recently proposed method to approximate hard optimization problems are demonstrated on the graph partitioning problem. The performance of this new method, called Extremal Optimization, is compared to Simulated Annealing in…
We show that there exist efficient algorithms for the triangle packing problem in colored permutation graphs, complete multipartite graphs, distance-hereditary graphs, k-modular permutation graphs and complements of k-partite graphs (when k…
Phylogenetic networks are increasingly used in evolutionary biology to represent the history of species that have undergone reticulate events such as horizontal gene transfer, hybrid speciation and recombination. One of the most fundamental…
Comparative analyses of phylogenetic trees typically require identical taxon sets, however, in practice, trees often include distinct but overlapping taxa. Pruning non-shared leaves discards phylogenetic signal, whereas tree completion can…
In the Properly Colored Spanning Tree problem, we are given an edge-colored undirected graph and the goal is to find a properly colored spanning tree, i.e., a spanning tree in which any two adjacent edges have distinct colors. The problem…
A \emph{binary tanglegram} is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential…
Matchings and coverings are central topics in graph theory. The close relationship between these two has been key to many fundamental algorithmic and polyhedral results. For mixed graphs, the notion of matching forest was proposed as a…
Strongly chordal graphs are a subclass of chordal graphs. Farber also established a number of different characterisations for this class of graphs. These include an intersection graph characterisation that is analogous to a similar…
Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…
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…
Perfect matchings and maximum weight matchings are two fundamental combinatorial structures. We consider the ratio between the maximum weight of a perfect matching and the maximum weight of a general matching. Motivated by the computer…
Phylogenetic trees play a key role in the reconstruction of evolutionary relationships. Typically, they are derived from aligned sequence data (like DNA, RNA, or proteins) by using optimization criteria like, e.g., maximum parsimony (MP).…
In this paper, we discuss the entanglement properties of graph-diagonal states, with particular emphasis on calculating the threshold for the transition between the presence and absence of entanglement (i.e. the separability point). Special…
A matching in a graph is uniquely restricted if no other matching covers exactly the same set of vertices. This notion was defined by Golumbic, Hirst, and Lewenstein and studied in a number of articles. Our contribution is twofold. We…