Related papers: Flipper games for monadically stable graph classes

Here we introduce a new game on graphs, called cup stacking, following a line of what can be considered as $0$-, $1$-, or $2$-person games such as chip firing, percolation, graph burning, zero forcing, cops and robbers, graph pebbling, and…

Stable gonality is a multigraph parameter that measures the complexity of a graph. It is defined using maps to trees. Those maps, in some sense, divide the edges equally over the edges of the tree; stable gonality asks for the map with the…

We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C*(G) is stable if and only if each vertex in G can be reached by an infinite…

In the graph sharing game, two players share a connected graph $G$ with non-negative weights assigned to the vertices, claiming and collecting the vertices of $G$ one by one, while keeping the set of all claimed vertices connected through…

This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…

We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the…

We present a linear stability analysis of stationary states (or fixed points) in large dynamical systems defined on random directed graphs with a prescribed distribution of indegrees and outdegrees. We obtain two remarkable results for such…

For a fixed graph $H$ and for arbitrarily large host graphs $G$, the number of homomorphisms from $H$ to $G$ and the number of subgraphs isomorphic to $H$ contained in $G$ have been extensively studied in extremal graph theory and graph…

Algorithmic graph theory has thoroughly analyzed how, given a network describing constraints between various nodes, groups can be formed among these so that the resulting configuration optimizes a \emph{global} metric. In contrast, for…

A vertex in a graph is said to be sedentary if a quantum state assigned on that vertex tends to stay on that vertex. Under mild conditions, we show that the direct product and join operations preserve vertex sedentariness. We also…

We consider monotonicity problems for graph searching games. Variants of these games - defined by the type of moves allowed for the players - have been found to be closely connected to graph decompositions and associated width measures such…

We show a simple method for constructing an infinite family of graph formation games with link bias so that the resulting games admits, as a \textit{pairwise stable} solution, a graph with an arbitrarily specified degree distribution.…

The dynamical properties of finite dynamical systems (FDSs) have been investigated in the context of coding theoretic problems, such as network coding, and in the context of hat games, such as the guessing game and Winkler's hat game. The…

We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually…

Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the…

Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of…

A sequence of graphs is FO-convergent if the probability of satisfaction of every first-order formula converges. A graph modeling is a graph, whose domain is a standard probability space, with the property that every definable set is Borel.…

We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…

Equistable graphs are graphs admitting positive weights on vertices such that a subset of vertices is a maximal stable set if and only if it is of total weight $1$. In $1994$, Mahadev et al.~introduced a subclass of equistable graphs,…

We introduce and study Maker/Breaker-type positional games on random graphs. Our main concern is to determine the threshold probability $p_{F}$ for the existence of Maker's strategy to claim a member of $F$ in the unbiased game played on…