25 papers · ranked by Valyu relevance
Christopher Duffy
We consider the problem of classifying those graphs that arise as an undirected square of an oriented graph by generalising the notion of quasi-transitive directed graphs to mixed graphs. We fully classify those graphs of maximum degree three and graphs of girth at least four that arise an undirected square of an…
Stacey McAdams, Jinko Kanno
A graph G has a k-page book embedding if G can be embedded into a k-page book. The minimum k such that G has a k-page book embedding is the book thickness of G, denoted bt(G). Most of the work on this subject has been done for unoriented graphs and oriented acyclic graphs (no directed cycles). In this work we discuss…
Nathan Reff
For a given hypergraph, an orientation can be assigned to the vertex-edge incidences. This orientation is used to define the adjacency and Laplacian matrices. In addition to studying these matrices, several related structures are investigated including the incidence dual, the intersection graph (line graph), and the…
Oswin Aichholzer, Jean Cardinal, Tony Huynh, Kolja Knauer + 3 more
'Torsten Mütze' 'Raphael Steiner' 'Birgit Vogtenhuber'] Flip graphs are a ubiquitous class of graphs, which encode relations on a set of combinatorial objects by elementary, local changes. Skeletons of associahedra, for instance, are the graphs induced by quadrilateral flips in triangulations of a convex polygon. For…
Benedict Paten, Adam M Novak, Erik Garrison, Glenn Hickey
A superbubble is a type of directed acyclic subgraph with single distinct source and sink vertices. In genome assembly and genetics, the possible paths through a superbubble can be considered to represent the set of possible sequences at a location in a genome. Bidirected and biedged graphs are a generalization of…
Carla Binucci, Walter Didimo, Maurizio Patrignani
The problem of orienting the edges of an undirected graph such that the resulting digraph is acyclic and has a single source s and a single sink t has a long tradition in graph theory and is central to many graph drawing algorithms. Such an orientation is called an st-orientation. We address the problem of computing…
Raffaella Mulas, Rubén J. Sánchez-García, Ben D. MacArthur
Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph representations only describe pairwise interactions between molecular species and so are…
Frank Gurski, Dominique Komander, Carolin Rehs
Coloring is one of the most famous problems in graph theory. The coloring problem on undirected graphs has been well studied, whereas there are very few results for coloring problems on directed graphs. An oriented k-coloring of an oriented graph G = (V, A) is a partition of the vertex set V into k independent sets…
Authors not listed
A directed graph (or digraph) consists of a finite vertex set 𝑉 and a set of ordered edges 𝐸 ⊆ 𝑉 × 𝑉, each edge (𝑢, 𝑣) indicating a one-way connection from 𝑢 (source) to 𝑣 (target). A bidirected graph is a generalization of an undirected graph where each edge is assigned a direction at each of its endpoints…
Alessio Conte, Roberto Grossi, Andrea Marino, Roméo Rizzi
Acyclic and cyclic orientations of an undirected graph have been widely studied for their importance: an orientation is acyclic if it assigns a direction to each edge so as to obtain a directed acyclic graph (DAG) with the same vertex set; it is cyclic otherwise. As far as we know, only the enumeration of acyclic…
Debajyoti Mondal, N. Parthiban, Indra Rajasingh
The diameter of an undirected or a directed graph is defined to be the maximum shortest path distance over all pairs of vertices in the graph. Given an undirected graph G, we examine the problem of assigning directions to each edge of G such that the diameter of the resulting oriented graph is minimized. The minimum…
Francesco Caravelli
Background Group field theory is an emerging field at the boundary between Quantum Gravity, Statistical Mechanics and Quantum Field Theory and provides a path integral for the gluing of n-simplices. Colored group field theory has been introduced in order to improve the renormalizability of the theory and associates…
Adam M. Novak, Erik Garrison, Benedict Paten
We present a generalization of the Positional Burrows-Wheeler Transform (PBWT) to genome graphs, which we call the gPBWT. A genome graph is a collapsed representation of a set of genomes described as a graph. In a genome graph, a haplotype corresponds to a restricted form of walk. The gPBWT is a compressible…
Authors not listed
Genetic Algorithms are a powerful method to solve optimization problems with complex cost functions over vast search spaces that rely in particular on recombining parts of previous solutions. Crossover operators play a crucial role in this context. Here, we describe a large class of these operators designed for…
Erich Kummerfeld, Anthony C Constantinou
Artificial intelligence for causal discovery frequently uses Markov equivalence classes of directed acyclic graphs, graphically represented as essential graphs, as a way of representing uncertainty in causal directionality. There has been confusion regarding how to interpret undirected edges in essential graphs…
Kuan-Hao Chao, Pei-Wei Chen, Sanjit A. Seshia, Ben Langmead
A Wheeler graph represents a collection of strings in a way that is particularly easy to index and query. Such a graph is a practical choice for representing a graph-shaped pangenome, and it is the foundation for current graph-based pangenome indexes. However, there are no practical tools to visualize or to check…
Lionel Zoubritzky, François-Xavier Coudert
We present here an open-source Julia library for the topological identification of crystalline materials, with algorithmic and computational improvements over the previously available software in the field, resulting in a speed increase of one order of magnitude. This new algorithm and implementation can therefore be…
Mikko Rautiainen, Tobias Marschall
Graphs are commonly used to represent sets of sequences. Either edges or nodes can be labeled by sequences, so that each path in the graph spells a concatenated sequence. Examples include graphs to represent genome assemblies, such as string graphs and de Bruijn graphs, and graphs to represent a pan-genome and hence…
Authors not listed
Previously we posited that a systematic and general description of stereoisomerism could be based upon the principles of the polytopal rearrangement model. The most daunting challenge to this end is to comprehensively describe all possible geometries for arbitrary n-coordinate centres, ABn, and for this we have…
Yohei Rosen, Jordan Eizenga, Benedict Paten
Analysis of genetic variation using graph structures is an emerging paradigm of genomics. However, defining genetic sites on sequence graphs remains an open problem. Paten’s invention of the ultra-bubble and snarl, special subgraphs of sequence graphs which can identified with efficient algorithms, represents important…
Zhaoyang Wang, Xianghui Fu, Bo Deng, Yang Chen + 1 more
In algebraic topology, a k-dimensional simplex is defined as a convex polytope consisting of k + 1 vertices. If spatial dimensionality is not considered, it corresponds to the complete graph with k + 1 vertices in graph theory. The alternating sum of the number of simplices across dimensions yields a topological…
Qichen Huang, Haoyang Guo
Cellular automata and graph reaction–diffusion systems encode local spatial interactions in different mathematical forms. We develop a cochain-operator calculus for these two settings. Over a finite field F_q_, every local rule on a finite neighborhood has a unique reduced polynomial representative. On an oriented…
Michael Hutcheon, Andrew Teale
Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighbourhood graph…
Peter Wills, François G. Meyer
Comparison of graph structure is a ubiquitous task in data analysis and machine learning, with diverse applications in fields such as neuroscience [1], cyber security [2], social network analysis [3], and bioinformatics [4], among others. Discovery and comparison of structures such as modular communities, rich clubs…
Andrea Savoini, Peter Gallagher, Abed Saady, John Maynard + 2 more
Mechanical stereochemistry arises when the interlocking of stereochemically trivial covalent subcomponents results in a stereochemical complex object. Although this general concept was identified in 1961, the stereochemical description of these molecules is still under development, with new mechanical stereoisomers…