相关论文: Graph labeling games

We investigate the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes. We insist on straight-line edges and crossing-free drawings. This problem has many connections…

Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of $k > 0$ colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial…

We present a novel approach for graph classification based on tabularizing graph data via new variants of the Weisfeiler-Leman algorithm and then applying methods for tabular data. The variants are obtained by modifying the underlying…

A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…

On one hand, compared with traditional relational and XML models, graphs have more expressive power and are widely used today. On the other hand, various applications of social computing trigger the pressing need of a new search paradigm.…

We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…

Graphs are ubiquitous in nature and can therefore serve as models for many practical but also theoretical problems. For this purpose, they can be defined as many different types which suitably reflect the individual contexts of the…

Graph Neural Networks (GNNs) have achieved state-of-the-art results in node classification tasks. However, most improvements are in multi-class classification, with less focus on the cases where each node could have multiple labels. The…

We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck…

We present a self-contained introduction to the theory of chip-firing games on metric graphs, as well as the more recent theory of tropical Prym varieties. We briefly discuss the connection between these notions and their algebraic…

We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a)…

While general game playing is an active field of research, the learning of game design has tended to be either a secondary goal of such research or it has been solely the domain of humans. We propose a field of research, Automated Game…

We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…

In this article, we extend several algebraic graph analysis methods to bipartite networks. In various areas of science, engineering and commerce, many types of information can be represented as networks, and thus the discipline of network…

We propose and analyse a 2-parameter family of 2-player games on two heaps of tokens, and present a strategy based on a class of sequences. The strategy looks easy, but is actually hard. A class of exotic numeration systems is then used,…

We have proposed a generalized quantization scheme for non-zero sum games which can be reduced to two existing quantization schemes under appropriate set of parameters. Some other important situations are identified which are not apparent…

The numbers game is a one-player game played on a finite simple graph with certain "amplitudes" assigned to its edges and with an initial assignment of real numbers to its nodes. The moves of the game successively transform the numbers at…

The abundance of interconnected data has fueled the design and implementation of graph generators reproducing real-world linking properties, or gauging the effectiveness of graph algorithms, techniques and applications manipulating these…

In this note we give a combinatorial characterization of all the unmixed bipartite graphs.

Binary classification problems can be naturally modeled as bipartite graphs, where we attempt to classify right nodes based on their left adjacencies. We consider the case of labeled bipartite graphs in which some labels and edges are not…