Related papers: Edge and Pair Queries -- Random Graphs and Complex…
Graph games lie at the algorithmic core of many automated design problems in computer science. These are games usually played between two players on a given graph, where the players keep moving a token along the edges according to…
In the Matching Cut problem we ask whether a graph $G$ has a matching cut, that is, a matching which is also an edge cut of $G$. We consider the variants Perfect Matching Cut and Disconnected Perfect Matching where we ask whether there…
Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of…
Graph neural networks (GNNs) have been successfully applied to learning representation on graphs in many relational tasks. Recently, researchers study neural architecture search (NAS) to reduce the dependence of human expertise and explore…
We equip the edges of a deterministic graph $H$ with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in $H$ satisfying the property that…
We consider the Stochastic Matching problem, which is motivated by applications in kidney exchange and online dating. In this problem, we are given an undirected graph. Each edge is assigned a known, independent probability of existence and…
Finding paths in graphs is a fundamental graph-theoretic task. In this work, we we are concerned with finding a path with some constraints on its length and the number of vertices neighboring the path, that is, being outside of and incident…
In this paper we explore mathematical tools that can be used to relate directed and undirected random graph models to each other. We identify probability spaces on which a directed and an undirected graph model are equivalent, and…
We investigate the analytic spread of binomial edge ideals of finite simple graphs. We provide tight bounds for this invariant in general. For special families of graphs (e.g., closed graphs, pseudo-forests), we compute the exact value for…
Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…
We give operational meaning to wave-particle duality in terms of discrimination games. Duality arises as a constraint on the probability of winning these games. The games are played with the aid of an n-port interferometer, and involve 3…
There is a growing need for methods which can capture uncertainties and answer queries over graph-structured data. Two common types of uncertainty are uncertainty over the attribute values of nodes and uncertainty over the existence of…
The semi-random graph process is a single-player game that begins with an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then adaptively selects a vertex…
Parity binomial edge ideals of simple undirected graphs are introduced. Unlike binomial edge ideals, they do not have square-free Gr\"obner bases and are radical if only if the graph is bipartite or the characteristic of the ground field is…
We consider the problem of fairly dividing a set of heterogeneous divisible resources among agents with different preferences. We focus on the setting where the resources correspond to the edges of a connected graph, every agent must be…
A matching is said to be disconnected if the saturated vertices induce a disconnected subgraph and induced if the saturated vertices induce a 1-regular graph. The disconnected and induced matching numbers are defined as the maximum…
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
We prove some partial results on the periodicity of billiard systems on graphs. The results specialize to the case of $n$ billiards with equal mass on the unit interval or circle traveling at the same speed.
Properties of graphs that can be characterized by the spectrum of the adjacency matrix of the graph have been studied systematically recently. Motivated by the complexity of these properties, we show that there are such properties for which…
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…