Related papers: On word-representability of simplified de Bruijn g…
Pangenomes serve as a framework for joint analysis of genomes of related organisms. Several pangenome models were proposed, offering different functionalities, applications provided by available tools, their efficiency etc. Among them, two…
The representation number of a graph is the minimum number of copies of each vertex required to represent the graph as a word, such that the letters corresponding to vertices $x$ and $y$ alternate if and only if $xy$ is an edge in the…
We define generalized de Bruijn words as those words having a Burrows-Wheeler transform that is a concatenation of permutations of the alphabet. We show that generalized de Bruijn words are in 1-to-1 correspondence with Hamiltonian cycles…
Consider a graph G = G(k,d,s) with vertex set the set of all k-letter words over an alphabet of size d. An edge e = vw is in E iff v is distinct from w and the last(first) k-s letters of v are identical to the first(last) k-s letters of w.…
This paper proves the existence of $t$-identifying codes on the class of undirected de Bruijn graphs with string length $n$ and alphabet size $d$, referred to as $\mathcal{B}(d,n)$. It is shown that $\mathcal{B}(d,n)$ is $t$-identifiable…
A generalized de Bruijn digraph generalizes a de Bruijn digraph to the case where the number of vertices need not be a pure power of an integer. Hamiltonian cycles in these digraphs thus generalize regular de~Bruijn cycles, and we will thus…
Several popular language models represent local contexts in an input text $x$ as bags of words. Such representations are naturally encoded by a sequence graph whose vertices are the distinct words occurring in $x$, with edges representing…
For positive integers $k,n$, a de Bruijn sequence $B(k,n)$ is a finite sequence of elements drawn from $k$ characters whose subwords of length $n$ are exactly the $k^n$ words of length $n$ on $k$ characters. This paper introduces the…
The graphs with permutation-representation number (\textit{prn}) at most two are known. While a characterization for the class of graphs with the \textit{prn} at most three is an open problem, we summarize the graphs of this class that are…
The first step in any genome assembly algorithm entails the conversion from the domain of strings and overlaps to the language of graphs and paths, typically using one of the two conventional methods: de Bruijn graphs or overlap graphs.…
The class of word-representable graphs, introduced in connection with the study of the Perkins semigroup by Kitaev and Seif, has attracted significant attention in combinatorics and theoretical computer science due to its deep connections…
The family of graphs of reduced words of a certain subcollection of permutations in the union $\cup_{n\geq 4}\frak{S}_{n}$ of symmetic groups is investigated. The subcollection is characterised by the hook cycle type $(n-2,1,1)$ with…
Graph-based semantic representations are valuable in natural language processing, where it is often simple and effective to represent linguistic concepts as nodes, and relations as edges between them. Several attempts has been made to find…
Graph-based text representation focuses on how text documents are represented as graphs for exploiting dependency information between tokens and documents within a corpus. Despite the increasing interest in graph representation learning,…
Variation graphs, which represent genetic variation within a population, are replacing sequences as reference genomes. Path indexes are one of the most important tools for working with variation graphs. They generalize text indexes to…
Let $G$ be a graph with vertex set $V(G)$. Let $n$ and $k$ be non-negative integers such that $n + 2k \leq |V(G)| - 2$ and $|V(G)| - n$ is even. If when deleting any $n$ vertices of $G$ the remaining subgraph contains a matching of $k$…
De novo DNA assembly is a fundamental task in Bioinformatics, and finding Eulerian paths on de Bruijn graphs is one of the dominant approaches to it. In most of the cases, there may be no one order for the de Bruijn graph that works well…
Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to…
In this paper, we discuss a method for identifying a seed word that would best represent a class of named entities in a graphical representation of words and their similarities. Word networks, or word graphs, are representations of…
String diagrams are a powerful tool for reasoning about composite structures in symmetric monoidal categories. By representing string diagrams as graphs, equational reasoning can be done automatically by double-pushout rewriting. !-graphs…