Related papers: On unavoidable sets of word patterns
The de Bruijn graph, its sequences, and their various generalizations, have found many applications in information theory, including many new ones in the last decade. In this paper, motivated by a coding problem for emerging memory…
A cornerstone of extremal graph theory due to Erd\H{o}s and Stone states that the edge density which guarantees a fixed graph $F$ as subgraph also asymptotically guarantees a blow-up of $F$ as subgraph. It is natural to ask whether this…
We prove that for a suitably nice class of random substitutions, their corresponding subshifts have automorphism groups that contain an infinite simple subgroup and a copy of the automorphism group of a full shift. Hence, they are…
Overlaps between words are crucial in many areas of computer science, such as code design, stringology, and bioinformatics. A self overlapping word is characterized by its periods and borders. A period of a word $u$ is the starting position…
I introduce a formalism for representing the syntax of recursively structured graph-like patterns. It does not use production rules, like a conventional graph grammar, but represents the syntactic structure in a more direct and declarative…
Given two graphs, a mapping between their edge-sets is cycle-continuous, if the preimage of every cycle is a cycle. The motivation for this notion is Jaeger's conjecture that for every bridgeless graph there is a cycle-continuous mapping to…
The notion of robust expansion has played a central role in the solution of several conjectures involving the packing of Hamilton cycles in graphs and directed graphs. These and other results usually rely on the fact that every robustly…
We study Hamilton cycles and perfect matchings in a uniform attachment graph. In this random graph, vertices are added sequentially, and when a vertex $t$ is created, it makes $k$ independent and uniform choices from $\{1,\dots,t-1\}$ and…
Human syntactic structures are usually represented as graphs. Much research has focused on the mapping between such graphs and linguistic sequences, but less attention has been paid to the shapes of the graphs themselves: their topologies.…
We develop a combinatorial approach to the study of semigroups and monoids with finite presentations satisfying small overlap conditions. In contrast to existing geometric methods, our approach facilitates a sequential left-right analysis…
A decomposition of a graph is a set of subgraphs whose edges partition those of $G$. The 3-decomposition conjecture posed by Hoffmann-Ostenhof in 2011 states that every connected cubic graph can be decomposed into a spanning tree, a…
Given an infinite word over the alphabet $\{0,1,2,3\}$, we define a class of bipartite hereditary graphs $\mathcal{G}^\alpha$, and show that $\mathcal{G}^\alpha$ has unbounded clique-width unless $\alpha$ contains at most finitely many…
This paper formulates a novel problem on graphs: find the minimal subset of edges in a fully connected graph, such that the resulting graph contains all spanning trees for a set of specifed sub-graphs. This formulation is motivated by an…
A double occurrence word $w$ over a finite alphabet $\Sigma$ is a word in which each alphabet letter appears exactly twice. Such words arise naturally in the study of topology, graph theory, and combinatorics. Recently, double occurrence…
We present a new recursive generation algorithm for prefix normal words. These are binary strings with the property that no substring has more 1s than the prefix of the same length. The new algorithm uses two operations on binary strings,…
In 1963, Anton Kotzig famously conjectured that $K_{n}$, the complete graph of order $n$, where $n$ is even, can be decomposed into $n-1$ perfect matchings such that every pair of these matchings forms a Hamilton cycle. The problem is still…
Binary time series data are very common in many applications, and are typically modelled independently via a Bernoulli process with a single probability of success. However, the probability of a success can be dependent on the outcome…
The nodes of the de Bruijn graph B(d,3) consist of all strings of length 3, taken from an alphabet of size d, with edges between words which are distinct substrings of a word of length 4. We give an inductive characterization of the maximum…
The paper explores combinatorial properties of Fibonacci words and their generalizations within the framework of combinatorics on words. These infinite sequences, measures the diversity of subwords in Fibonacci words, showing non-decreasing…
We prove new lower bounds on the crossing number of a complete graphs assuming that it is drawn in such a way that it contains a Hamiltonian cycle with no crossings.