A threshold for the Maker-Breaker clique game - Department of
edges of a k-clique; Breaker wins otherwise. We determine that the threshold for the graph property that Maker can win this game is at n− 2 k+1 , for all k > 3, thus ...
A threshold for the Maker-Breaker clique game
Oct 7, 2012 ... all the edges of a k-clique; Breaker wins otherwise. We determine that the threshold for the graph property that Maker can win this game is at n− ...
A threshold for the MakerBreaker clique game - Wiley Online Library
Mar 5, 2013 ... ABSTRACT: We study the Maker-Breaker k-clique game played on the .... Maker wins the k-clique game on G(n, p) a.a.s. The threshold for the ...
Positional Games - School of Mathematical Sciences
Breaker version of the clique game (Kn,Kq), Maker wins if in the end of the game ..... We conclude that the threshold bias for all games on Kn, where all winning.
A remark on the tournament game - The Electronic Journal of
Mar 29, 2015 ... We study the Maker-Breaker tournament game played on the edge set of a given ... clique game on Kn, Maker has a strategy to occupy a clique of size (2 ... the threshold probability pF such that for p = ω(pF ) the game (E(Gn ...
Positional games on random graphs
Mar 19, 2005 ... We introduce and study Maker/Breaker-type positional games on ran- ... For the family Kk = Kk,n of all k-cliques on n vertices, Bednarska and ... threshold for the appearance of the first element of F in the random graph.
arXiv:math/0601659v1 [math.CO] 26 Jan 2006 - arXiv.org
Jan 26, 2006 ... Abstract. We introduce and study Maker/Breaker-type positional games on ran- dom graphs. Our main concern is to determine the threshold probability. pF for the ... clique game and the Hamiltonian cycle game. 1 Introduction.
Positional games on graphs
Dec 21, 2010 ... We study Maker-Breaker games played on the edges of the complete graph on n vertices ... threshold bias bF (a) for all values of a, so that for every b, b ≤ bF (a), Maker wins the ...... proved that in the (1 : 1) q-clique game, K q.
On the Clique-Game - CiteSeerX
We study Maker/Breaker games on the edges of the complete graph, as ... (2−o(1 )) log N, thus the threshold where the random q-clique game turns from a ...
ON THE THRESHOLD FOR THE MAKER-BREAKER H-GAME
Jan 17, 2014 ... We study the Maker-Breaker H-game played on the edge set of the ... For the case that H is a clique such thresholds were recently obtained by ...
Maker-Breaker games on random geometric graphs - Macalester
Sep 21, 2013 ... In a Maker-Breaker game on a graph G, Breaker and Maker alternately ..... threshold for the appearance of a clique on which Maker can win the ...
Maker-Breaker games on random geometric graphs - Department of
May 2, 2014 ... In a Maker-Breaker game on a graph G, Breaker and Maker alternately ..... threshold for the appearance of a clique on which Maker can win the ...
Maker-Breaker Games on Random Geometric Graphs - Eurandom
Jan 8, 2014 ... Sharp Threshold for the Hamilton Cycle Maker-Breaker game, 2009. ... Hitting Time Results for Maker-Breaker Games, 2011. Maker-Breaker .... Dangerous Cluster: a maximal clique of dangerous points. Maker-Breaker ...
On the Chvátal-Erd˝os triangle game
Oct 13, 2010 ... Chvátal and Erd˝os  asked about the threshold for the bias q in such ... edge set of the complete graph Kn in which Maker and Breaker .... I. At the end of each round, after Breaker's move, for every vertex v, NM (v) is a clique.
Fast Strategies In Maker-Breaker Games Played - MIT Mathematics
Mar 15, 2012 ... Maker-Breaker games played on the edge set of the complete graph Kn are well studied. In ... game, the connectivity game and the k-clique game. ... threshold probability for the property of Gn,p having an isolated vertex.
Planarity, colorability and minor games - Semantic Scholar
Aug 30, 2007 ... While the similar threshold bF does exist for Maker/Breaker games on ..... edges are the ⌈n/k⌉-cliques of Kn. We name the players of the (b,1,F) ...
Humberto Naves – Curriculum Vitae - Institute for Mathematics and
the minimum number of k-cliques, J. Combinatorial Theory Ser. B 103 (2013) ... Maker-Breaker games, Randon Structures and Algorithms, to appear. ...  R. Glebov, H. Naves, and B. Sudakov, The threshold probability for long cycles,.
On Combinatorial Problems of Extremal Nature and Games
method lies in the field of positional games, more specifically Maker-Breaker .... density in any graph with no cliques of size r is attained by an r − 1 partite graph. ..... for threshold graphs and Section 2.4 contains the proof of the stability result.
Existence and Enumeration of Spanning Structures in - TUBdok
4.3.1 Local resilience of hypergraphs and Maker-Breaker games . .... multigraphs where each of the colour classes induces a disjoint union of cliques and we prove .... Furthermore, the threshold for a monotone increasing property P is defined ...
c 2012 by Jane Victoria Butterfield. All rights reserved. - Ideals
into k cliques and independent sets and provide a characterization. ... When k > 2 , these upper bounds provide the first separation from the offline threshold. ..... Many other positional games have been studied, including Maker/Breaker games .
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