Related papers: Graph labeling games

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…

Probabilistic concurrent/distributed strategies have so far not been investigated thoroughly in the context of imperfect information, where the Player has only partial knowledge of the moves made by the Opponent. In a situation where the…

A graceful labeling of a graph $G$ with $m$ edges consists of labeling the vertices of $G$ with distinct integers from $0$ to $m$ such that, when each edge is assigned as induced label the absolute difference of the labels of its endpoints,…

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 introduce a new graph polynomial in two variables. This ``interlace'' polynomial can be computed in two very different ways. The first is an expansion analogous to the state space expansion of the Tutte polynomial; the significant…

Adding game elements to higher education is an increasingly common practice. As a result, many recent empirical studies focus on studying the effectiveness of gamified or game-based educational experiences. The findings of these studies are…

This paper surveys a comprehensive, although not exhaustive, sampling of graph polynomials with the goal of providing a brief overview of a variety of techniques defining a graph polynomial and then for decoding the combinatorial…

This paper deals with the $\lambda$-labeling and $L(2,1)$-coloring of simple graphs. A $\lambda$-labeling of a graph $G$ is any labeling of the vertices of $G$ with different labels such that any two adjacent vertices receive labels which…

Graphs are structured data that models complex relations between real-world entities. Heterophilic graphs, where linked nodes are prone to be with different labels or dissimilar features, have recently attracted significant attention and…

We study free scalar field theory on a graph, which gives rise to a modified version of discrete Green's function on a graph studied in \cite{CY}. We show that this gives rise to a graph invariant, which is closely related to the 2-dim…

A labelling of a graph is an assignment of labels to its vertex or edge sets (or both), subject to certain conditions, a well established concept. A labelling of a graph G of order n is termed a numbering when the set of integers {1,...,n}…

Drawing network maps automatically comprises two challenging steps, namely laying out the map and placing non-overlapping labels. In this paper we tackle the problem of labeling an already existing network map considering the application of…

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented…

It is well-known that exploiting label correlations is important to multi-label learning. Existing approaches either assume that the label correlations are global and shared by all instances; or that the label correlations are local and…

We introduce the class of modified Schelling games in which there are different types of agents who occupy the nodes of a location graph; agents of the same type are friends, and agents of different types are enemies. Every agent is…

Domination game [SIAM J.\ Discrete Math.\ 24 (2010) 979--991] and total domination game [Graphs Combin.\ 31 (2015) 1453--1462] are by now well established games played on graphs by two players, named Dominator and Staller. In this paper,…

Graph-structured data, prevalent in domains ranging from social networks to biochemical analysis, serve as the foundation for diverse real-world systems. While graph neural networks demonstrate proficiency in modeling this type of data,…

Automated game design is a rapidly growing area of research, yet many aspects of game design lie largely unexamined still, as most systems focus on two-dimensional games with clear objectives and goal-oriented gameplay. This paper describes…

We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of…

We prove new lower and upper bounds on the higher gonalities of finite graphs. These bounds are generalizations of known upper and lower bounds for first gonality to higher gonalities, including upper bounds on gonality involving…