Related papers: Path sets in one-sided symbolic dynamics

This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent…

We consider Independent Set and Dominating Set restricted to VPG graphs (or, equivalently, string graphs). We show that they both remain $\mathsf{NP}$-hard on $B_0$-VPG graphs admitting a representation such that each grid-edge belongs to…

We develop some aspects of a general theory of presentations of subshifts by labelled directed graphs, in particular by compact graphs. Also considered are synchronization properties of subshifts that lead to presentations by countable…

A biased graph consists of a graph $G$ together with a collection of distinguished cycles of $G$, called balanced cycles, with the property that no theta subgraph contains exactly two balanced cycles. Perhaps the most natural biased graphs…

We define a notion of (one-sided) shift spaces over infinite alphabets. Unlike many previous approaches to shift spaces over countable alphabets, our shift spaces are compact Hausdorff spaces. We examine shift morphisms between these shift…

We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertex-transitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle…

The intersection graph of a family of sets $\{S_{1},S_{2},\ldots,S_{n}\}$ is a graph whose vertex set is $\{S_{1},S_{2},\ldots,S_{n}\}$ and two distinct vertices are adjacent if the intersection of the corresponding sets is non-empty.…

We characterize geodesic paths in the $n$-dimensional unit sphere under sup norm. A geodesic path between two points is a shortest curve joining the two points.

Gain graphs are graphs where the edges are given some orientation and labeled with the elements (called gains) from a group so that gains are inverted when we reverse the direction of the edges. Generalizing the notion of gain graphs, skew…

Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter $\alpha$, called the pathway parameter, one can connect generalized type-1 beta family…

Let $\pi$ be a non-degenerate permutation on at least $4$ symbols. We show that the set of uniquely ergodic interval exchange transformations with permutation $\pi$ is path-connected.

While routinely used in other areas of dynamics, image sets are ill-defined objects in general non-invertible measurable dynamics. We propose a way of consistently working with image sets of null-preserving (and hence, in particular, of…

Given a graph G equals (V,E), a subset S subset of V is a dominating set if every vertex in V minus S is adjacent to some vertex in S. The dominating set with the least cardinality, gamma, is called a gamma-set which is commonly known as a…

A signed graph is a graph together with an assignment of signs to the edges. A closed walk in a signed graph is said to be positive (negative) if it has an even (odd) number of negative edges, counting repetition. Recognizing the signs of…

In this paper we further develop the theory of one sided shift spaces over infinite alphabets, characterizing one-step shifts as edge shifts of ultragraphs and partially answering a conjecture regarding shifts of finite type (we show that…

We develop a directional formalism for the partition graph G_n based on several canonical reference sets: the main chain, the self-conjugate axis, the spine, and the boundary framework. For each such set S, the graph distance d_S induces a…

Let $G$ be a complete graph with $n+1$ vertices. In a recent paper of the authors, it is shown that the path trees of the graph play a special role in the structure of the truncated powers and partition functions that are associated with…

For a degree sequence, we define the set of edges that appear in every labeled realization of that sequence as forced, while the edges that appear in none as forbidden. We examine structure of graphs whose degree sequences contain either…

We characterize the fixed sets of automorphisms of an arbitrary countable, arithmetically saturated structure.

One model of message delivery in a computer network is based on labelling each edge by a subset of a (reasonably small) universal set, and then encoding a path as the union of the labels of its edges. Earlier work suggested using random…