相关论文: Chip-Firing and Riemann-Roch Theory for Directed G…

Parikh's game logic is a PDL-like fixpoint logic interpreted on monotone neighbourhood frames that represent the strategic power of players in determined two-player games. Game logic translates into a fragment of the monotone…

Graph minors are a primary tool in understanding the structure of undirected graphs, with many conceptual and algorithmic implications. We propose new variants of \emph{directed graph minors} and \emph{directed graph embeddings}, by…

We generalize Brownian motion on a Riemannian manifold to the case of a family of metrics which depends on time. Such questions are natural for equations like the heat equation with respect to time dependent Laplacians (inhomogeneous…

In 2021, Adam Zsolt Wagner proposed an approach to disprove conjectures in graph theory using Reinforcement Learning (RL). Wagner's idea can be framed as follows: consider a conjecture, such as a certain quantity f(G) < 0 for every graph G;…

The traditional game of cops and robbers is played on undirected graph. Recently, the same game played on directed graph is getting attention by more and more people. We knew that if we forbid some subgraph we can bound the cop number of…

We develop the theory of linear evolution equations associated with the adjacency matrix of a graph, focusing in particular on infinite graphs of two kinds: uniformly locally finite graphs as well as locally finite line graphs. We discuss…

Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood.…

A modeloid, a certain set of partial bijections, emerges from the idea to abstract from a structure to the set of its partial automorphisms. It comes with an operation, called the derivative, which is inspired by Ehrenfeucht-Fra\"iss\'e…

Cat-and-mouse is a two-player game on a finite graph. Chandra and Stockmeyer showed cat-and-mouse is P-complete on directed graphs. We show cat-and-mouse is P-complete on undirected graphs. To our knowledge, no proof of the directed case…

Recently, bidirected graphs have received increasing attention from the graph theory community with both structural and algorithmic results. Bidirected graphs are a generalization of directed graphs, consisting of an undirected graph…

Given two distributions F and G on the nonnegative integers we propose an algorithm to construct in- and out-degree sequences from samples of i.i.d. observations from F and G, respectively, that with high probability will be graphical, that…

The present paper is the first one in the sequence of papers about a simple class of {\em framed $4$-graphs}; the goal of the present paper is to collect some well-known results on planarity and to reformulate them in the language of {\em…

We consider the pursuit and evasion game on finite, connected, undirected graphs known as cops and robbers. Meyniel conjectured that for every graph on n vertices a rootish number of cops can win the game. We prove that this holds up to a…

We introduce a class of graphs called compound graphs, generalizing rectangles, which are constructed out of copies of a planar bipartite base graph. The main result is that the number of perfect matchings of every compound graph is…

This paper explores the properties of directed graphs, termed generalized action graphs, which exhibit a strong connection to certain number sequences. Focusing on the structural and combinatorial aspects, we investigate the conditions…

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…

This article contributes to the discussion on the relationship between the Neyman-Rubin and the graphical frameworks for causal inference. We present specific examples of data-generating mechanisms - such as those involving undirected or…

Multiplayer games on graphs are at the heart of theoretical descriptions of key evolutionary processes that govern vital social and natural systems. However, a comprehensive theoretical framework for solving multiplayer games with an…

An $n$-player game $X$ in normal form can be modeled via undirected discrete graphical models where the discrete random variables represent the players and their state spaces are the set of pure strategies. There exists an edge between the…

We consider hereditary classes of graphs equipped with a total order. We provide multiple equivalent characterisations of those classes which have bounded twin-width. In particular, we prove a grid theorem for classes of ordered graphs…