Three-player Col played on trees is NP-complete
نویسنده
چکیده
The game of Col is a two-player mapcoloring game invented by Colin Vout where to establish who has a winning strategy on a general graph is a PSPACE-complete problem. However, winning strategies can be found on specific graph instances, e.g., k-ary complete trees. Three-player Col is a threeplayer version of Col. Because of the possibility to form alliances, cooperation between players is a keyfactor to determine the winning coalition and, as a result, three-player Col played on trees is NP-complete.
منابع مشابه
Sankaku-Tori: An Old Western-Japanese Game Played on a Point Set
We study a combinatorial game named “sankaku-tori” in Japanese, which means “triangle-taking” in English. It is an old penciland-paper game for two players played in Western Japan. The game is played on points on the plane in general position. In each turn, a player adds a line segment to join two points, and the game ends when a triangulation of the point set is completed. The player who compl...
متن کاملThe Complexity of Request-Response Games
We consider two-player graph games whose objectives are request-response condition, i.e conjunctions of conditions of the form “if a state with property Rq is visited, then later a state with property Rp is visited”. The winner of such games can be decided in EXPTIME and the problem is known to be NP-hard. In this paper, we close this gap by showing that this problem is, in fact, EXPTIME-comple...
متن کاملYoung Reseachers Forum: Book of Abstracts
2048 is a single-player online puzzle game that went viral in March 2014. The game is played on a 4 × 4 board by sliding around and merging equal valued tiles to create tiles of higher value. The player wins by creating the 2048 valued tile, hence the name. We study the complexity of a slightly adapted version and prove that a number of natural decision problems turn out to be NP-Complete. We r...
متن کاملGame Values and Computational Complexity: An Analysis via Black-White Combinatorial Games
A black-white combinatorial game is a two-person game in which the pieces are colored either black or white. The players alternate moving or taking elements of a specific color designated to them before the game begins. A player loses the game if there is no legal move available for his color on his turn. We first show that some black-white versions of combinatorial games can only assume combin...
متن کاملThe Voronoi game on graphs and its complexity
The Voronoi game is a two-person game which is a model for a competitive facility location. The game is played on a continuous domain, and only two special cases (one-dimensional case and one-round case) are well investigated. We introduce the discrete Voronoi game in which the game arena is given as a graph. We first analyze the game when the arena is a large complete k-ary tree, and give an o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009