相关论文: The Zero Forcing Number of Twisted Hypercubes

The minimum forcing number of a graph $G$ is the smallest number of edges simultaneously contained in a unique perfect matching of $G$. Zhang, Ye and Shiu \cite{HDW} showed that the minimum forcing number of any fullerene graph was bounded…

A graph is cubical if it is a subgraph of a hypercube. For a cubical graph $H$ and a hypercube $Q_n$, $ex(Q_n, H)$ is the largest number of edges in an $H$-free subgraph of $Q_n$. If $ex(Q_n, H)$ is at least a positive proportion of the…

Gentner and Rautenbach conjectured that the size of a minimum zero forcing set in a connected graph on $n$ vertices with maximum degree $3$ is at most $\frac{1}{3}n+2$. We disprove this conjecture by constructing a collection of connected…

The global forcing number of a graph G is the minimal cardinality of an edge subset discriminating all perfect matchings of G, denoted by gf(G). For any perfect matching M of G, the minimal cardinality of an edge subset S in E(G)-M such…

The forcing number of a graph with a perfect matching $M$ is the minimum number of edges in $M$ whose endpoints need to be deleted, such that the remaining graph only has a single perfect matching. This number is of great interest in…

In the study of three-dimensional gapped models, two-dimensional gapped states should be considered as a free resource. This is the basic idea underlying the notion of `foliated fracton order' proposed in Phys. Rev. X 8, 031051 (2018). We…

While a number of bounds are known on the zero forcing number $Z(G)$ of a graph $G$ expressed in terms of the order of a graph and maximum or minimum degree, we present two bounds that are related to the (upper) total domination number…

We consider the triangle-free process: given an integer n, start by taking a uniformly random ordering of the edges of the complete n-vertex graph K_n. Then, traverse the ordered edges and add each traversed edge to an (initially empty)…

The anti-forcing number of a connected graph $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching. In this paper, we show that the anti-forcing number of every…

In a simple drawing of a graph, any two edges intersect in at most one point (either a common endpoint or a proper crossing). A simple drawing is generalized twisted if it fulfills certain rather specific constraints on how the edges are…

We define and investigate a quantisation of null hypersurfaces in the context of loop quantum gravity on a fixed graph. The main tool we use is the parametrisation of the theory in terms of twistors, which has already proved useful in…

In this paper, we define a new construction of completely scrambled 0-dimensional systems using the inverse limit of sequences of directed graph covers. These examples are transitive and are not locally equicontinuous.

A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative…

Irredundance has been studied in the context of dominating sets, via the concept of private neighbor. Here irredundance of zero forcing sets is introduced via the concept of a private fort and the upper and lower zero forcing irrdedundance…

Let $S$ be a set of vertices of a graph $G$. Let $cl(S)$ be the set of vertices built from $S$, by iteratively applying the following propagation rule: if a vertex and all but exactly one of its neighbors are in $cl(S)$, then the remaining…

We introduce a new model of indeterminacy in graphs: instead of specifying all the edges of the graph, the input contains all triples of vertices that form a connected subgraph. In general, different (labelled) graphs may have the same set…

There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both parameters with a third one, the algebraic co-rank; that is defined as the largest $i$ such that the $i$-th critical…

The Colouring problem is that of deciding, given a graph $G$ and an integer $k$, whether $G$ admits a (proper) $k$-colouring. For all graphs $H$ up to five vertices, we classify the computational complexity of Colouring for…

This paper studies the problem of designing networks that are strong structurally controllable, and robust simultaneously. For given network specifications, including the number of nodes $N$, the number of leaders $N_L$, and diameter $D$,…

We study the probabilistic zero forcing process, a probabilistic variant of the classical zero forcing process. We show that for every connected graph $G$ on $n$ vertices, there exists an initial set consisting of a single vertex such that…