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pro vyhledávání: '"05C57, 91A43"'
All roads lead to Rome is the core idea of the puzzle game Roma. It is played on an $n \times n$ grid consisting of quadratic cells. Those cells are grouped into boxes of at most four neighboring cells and are either filled, or to be filled, with arr
Externí odkaz:
http://arxiv.org/abs/2207.09439
Autor:
Lasoń, Michał
Publikováno v:
Random Structures & Algorithms 59 (2021), no. 2, 267-287
We study a new optimal stopping problem: Let $G$ be a fixed graph with $n$ vertices which become active on-line in time, one by another, in a random order. The active part of $G$ is the subgraph induced by the active vertices. Find a stopping algorit
Externí odkaz:
http://arxiv.org/abs/2001.07870
Autor:
Bonato, Anthony, Breen, Jane, Brimkov, Boris, Carlson, Joshua, English, Sean, Geneson, Jesse, Hogben, Leslie, Perry, K. E., Reinhart, Carolyn
The cop throttling number $th_c(G)$ of a graph $G$ for the game of Cops and Robbers is the minimum of $k + capt_k(G)$, where $k$ is the number of cops and $capt_k(G)$ is the minimum number of rounds needed for $k$ cops to capture the robber on $G$ ov
Externí odkaz:
http://arxiv.org/abs/1903.10087
Autor:
Offner, David, Ojakian, Kerry
We compare two kinds of pursuit-evasion games played on graphs. In Cops and Robbers, the cops can move strategically to adjacent vertices as they please, while in a new variant, called deterministic Zombies and Survivors, the zombies (the counterpart
Externí odkaz:
http://arxiv.org/abs/1809.03049
Autor:
Epperlein, Jeremias, Švígler, Vladimír
A periodic behavior is a well observed phenomena in biological and economical systems. We show that evolutionary games on graphs with imitation dynamics can display periodic behavior for an arbitrary choice of game theoretical parameters describing s
Externí odkaz:
http://arxiv.org/abs/1805.03849
We define a two-player combinatorial game in which players take alternate turns; each turn consists on deleting a vertex of a graph, together with all the edges containing such vertex. If any vertex became isolated by a player's move then it would al
Externí odkaz:
http://arxiv.org/abs/1507.05673
Autor:
Schmidt, Simon
The $3/5$-conjecture for the domination game states that the game domination numbers of an isolate-free graph $G$ on $n$ vertices are bounded as follows: $\gamma_g(G)\leq \frac{3n}5 $ and $\gamma_g'(G)\leq \frac{3n+2}5 $. Recent progress have been do
Externí odkaz:
http://arxiv.org/abs/1507.02875
Autor:
Cheng, Yukun, Zhou, Sanming
Publikováno v:
Advances in Global Optimization, Springer Proceedings in Mathematics & Statistics Volume 95, 2015, pp 117-128
In a facility game one or more facilities are placed in a metric space to serve a set of selfish agents whose addresses are their private information. In a classical facility game, each agent wants to be as close to a facility as possible, and the co
Externí odkaz:
http://arxiv.org/abs/1503.07426
We introduce a game on graphs. By a theorem of Zermelo, each instance of the game on a finite graph is determined. While the general decision problem on which player has a winning strategy in a given instance of the game is unsolved, we solve the dec
Externí odkaz:
http://arxiv.org/abs/1411.5429
Autor:
Bujtás, Csilla, Tuza, Zsolt
We introduce and study a Maker-Breaker type game in which the issue is to create or avoid two disjoint dominating sets in graphs without isolated vertices. We prove that the maker has a winning strategy on all connected graphs if the game is started
Externí odkaz:
http://arxiv.org/abs/1411.5184