Related papers: P_3-Games
Many polynomial invariants are defined on graphs for encoding the combinatorial information and researching them algebraically. In this paper, we introduce the cycle polynomial and the path polynomial of directed graphs for counting cycles…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
We consider the $n\times n$ game of Phutball. It is shown that, given an arbitrary position of stones on the board, it is a PSPACE-hard problem to determine whether the specified player can win the game, regardless of the opponent's choices…
The paper introduces two player connectivity games played on finite bipartite graphs. Algorithms that solve these connectivity games can be used as subroutines for solving M\"uller games. M\"uller games constitute a well established class…
In general, finite concurrent two-player reachability games are only determined in a weak sense: the supremum probability to win can be approached via stochastic strategies, but cannot be realized. We introduce a class of concurrent games…
This paper introduces a collection of board games specifically chosen to serve as a basis for programming exercises. We examine the attractiveness of board games in this context as well as features that make a particular game a good…
The family of cycle completable graphs has several cryptomorphic descriptions, the equivalence of which has heretofore been proven by a laborious implication-cycle that detours through a motivating matrix completion problem. We give a…
Fractional hedonic games are coalition formation games where a player's utility is determined by the average value they assign to the members of their coalition. These games are a variation of graph hedonic games, which are a class of…
The interactive game theoretical approach to the description of perception processes is proposed. The subject is treated formally in terms of a new class of the verbalizable interactive games which are called the perception games. An…
Fay, Hurlbert and Tennant recently introduced a one-player game on a finite connected graph $G$, which they called cup stacking. Stacks of cups are placed at the vertices of $G$, and are transferred between vertices via stacking moves,…
The reversible pebble game is a combinatorial game played on rooted DAGs. This game was introduced by Bennett (1989) motivated by applications in designing space efficient reversible algorithms. Recently, Chan (2013) showed that the…
A matching cut is a matching that is also an edge cut. In the problem Minimum Matching Cut, we ask for a matching cut with the minimum number of edges in the matching. We investigate the differences in complexity between Minimum Matching…
Arboreal categories were introduced as an axiomatic framework for game comonads, which provide a comonadic view on many model-comparison games in logic. We demonstrate the inadequacy of the axiom stating that paths are connected. We then…
Parity games are infinite two-player games played on directed graphs. Parity game solvers are used in the domain of formal verification. This paper defines parametrized parity games and introduces an operation, Justify, that determines a…
We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…
Consider equipping an alphabet $\mathcal{A}$ with a group action that partitions the set of words into equivalence classes which we call patterns. We answer standard questions for the Penney's game on patterns and show non-transitivity for…
Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and…
We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals:…
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
The top tree data structure is an important and fundamental tool in dynamic graph algorithms. Top trees have existed for decades, and today serve as an ingredient in many state-of-the-art algorithms for dynamic graphs. In this work, we give…