Related papers: The Identifying Code problem on $P_4$-tidy graphs
An identifying code in a graph is a subset of vertices having a nonempty and distinct intersection with the closed neighborhood of every vertex. We prove that the infimum density of any identifying code in $S_k$ (an infinite strip of $k$…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
This paper introduces the concept of compliant vertices and compliant graphs, with a focus on the total domination degree (TDD) of a vertex in compliant graphs. The TDD is systematically calculated for various graph classes, including path…
Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we…
We show that the problem of counting perfect matchings remains #P-complete even if we restrict the input to very dense graphs, proving the conjecture in [5]. Here "dense graphs" refer to bipartite graphs of bipartite independence number…
Recently, several vertex identifying notions were introduced (identifying coloring, lid-coloring, ...), these notions were inspired by identifying codes. All of them, as well as original identifying code, are based on separating two…
Identifying codes were introduced by Karpovsky et al. as dominating sets $S\subseteq V(G)$ satisfying $N[u]\cap S \neq N[v]\cap S$ for any distinct vertices $u,v$. Later, Junnila et al. introduced the concept of \emph{self-identifying…
Graph colorings have been of interest to mathematicians for a long time, but relatively recently, social scientists have also found them to be interesting tools for studying group behavior. In the last 20 years, scientists have begun to…
Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its…
This paper is mainly a semi-tutorial introduction to elementary algebraic topology and its applications to Ising-type models of statistical physics, using graphical models of linear and group codes. It contains new material on systematic…
Can we use machine learning to compress graph data? The absence of ordering in graphs poses a significant challenge to conventional compression algorithms, limiting their attainable gains as well as their ability to discover relevant…
We consider the problem of a graph subjected to adversarial perturbations, such as those arising from cyber-attacks, where edges are covertly added or removed. The adversarial perturbations occur during the transmission of the graph between…
An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from all other vertices by the set of vertices in C that are at distance at most 1 from x. The problem of finding an identifying code of…
Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are $\rm W[1]$-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including…
In the network activation problem, each edge in a graph is associated with an activation function, that decides whether the edge is activated from node-weights assigned to its end-nodes. The feasible solutions of the problem are the…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
It is well-known that the graph isomorphism problem can be posed as an equivalent problem of determining whether an auxiliary graph structure contains a clique of specific order. However, the algorithms that have been developed so far for…
While stabilizer tableaus have proven useful as a descriptive tool for additive quantum codes, they otherwise offer little guidance for concrete constructions or algorithm analysis. We introduce a representation of stabilizer codes as…
Graphs are ubiquitous data structures for representing interactions between entities. With an emphasis on the use of graphs to represent chemical molecules, we explore the task of learning to generate graphs that conform to a distribution…
A dominating set of a graph is a set of vertices such that every vertex not in the set has at least one neighbor in the set. The problem of counting dominating sets is #P-complete for chordal graphs but solvable in polynomial time for its…