منابع مشابه
Bichromatic Triangle Games
We study a combinatorial game called Bichromatic Triangle Game, defined as follows. Two players R and B construct a triangulation on a given planar point set V . Starting from no edges, players R and B take turns drawing one edge that connects two points in V . Player R uses color red and player B uses color blue. The first player who completes one empty monochromatic triangle is the winner. We...
متن کاملOn Bichromatic Triangle Game
We study a combinatorial game called Bichromatic Triangle Game, defined as follows. Two players R and B construct a triangulation on a given planar point set V . Starting from no edges, they take turns drawing one straight edge that connects two points in V and does not cross any of the previously drawn edges. PlayerR uses color red and player B uses color blue. The first player who completes o...
متن کاملGames on the Sperner Triangle
We create a new two-player game on the Sperner Triangle based on Sperner’s lemma. Our game has simple rules and several desirable properties. First, the game is always certain to have a winner. Second, like many other interesting games such as Hex and Geography, we prove that deciding whether one can win our game is a PSPACE-complete problem. Third, there is an elegant balance in the game such ...
متن کاملConnected, Bounded Degree, Triangle Avoidance Games
We consider variants of the triangle-avoidance game first defined by Harary and rediscovered by Hajnal a few years later. A graph game begins with two players and an empty graph on n vertices. The two players take turns choosing edges within Kn, building up a simple graph. The edges must be chosen according to a set of restrictions R. The winner is the last player to choose an edge that does no...
متن کاملGuessing Games on Triangle-Free Graphs
The guessing game introduced by Riis [Electron. J. Combin. 2007] is a variant of the “guessing your own hats” game and can be played on any simple directed graph G on n vertices. For each digraph G, it is proved that there exists a unique guessing number gn(G) associated to the guessing game played on G. When we consider the directed edge to be bidirected, in other words, the graph G is undirec...
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ژورنال
عنوان ژورنال: Electronic Notes in Discrete Mathematics
سال: 2011
ISSN: 1571-0653
DOI: 10.1016/j.endm.2011.05.019