منابع مشابه
Transitive Avoidance Games
Positional games are a well-studied class of combinatorial games. In their usual form, two players take turns to play moves in a set (‘the board’), and certain subsets are designated as ‘winning’: the first person to occupy such a set wins the game. For these games, it is well known that (with correct play) the game cannot be a second-player win. In the avoidance (or misère) form, the first per...
متن کاملThe Ehrenfeucht-Fraisse Games for Transitive Closure
We present in this paper Ehrenfeucht-Frai"sse games for the transitiveclosure logics DTC, TC and ATC. Although the existence of such games for logics with generalized quantifiers was known before, the exact formulation of these games for the predicate transformers arising from various transitive-closure-like operations is new. The games are sound and complete both for finite and infinite models...
متن کاملOnline balanced graph avoidance games
We introduce and study online balanced coloring games on the random graph process. The game is played by a player we call Painter. Edges of the complete graph with n vertices are introduced two at the time, in a random order. For each pair of edges, Painter immediately and irrevocably chooses one of the two possibilities to color one of them red and the other one blue. His goal is to avoid crea...
متن کاملResults on Pattern Avoidance Games
A zero-one matrix A contains another zero-one matrix P if some submatrix of A can be transformed to P by changing some ones to zeros. A avoids P if A does not contain P. The Pattern Avoidance Game is played by two players. Starting with an all-zero matrix, two players take turns changing zeros to ones while keeping A avoiding P. We study the strategies of this game for some patterns P. We also ...
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...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/6299