TY - JOUR
T1 - Weak and strong k-connectivity games
AU - Ferber, Asaf
AU - Hefetz, Dan
N1 - Funding Information:
This research of Dan Hefetz was supported by an EPSRC Institutional Sponsorship Fund.
PY - 2014/1
Y1 - 2014/1
N2 - For a positive integer k, we consider the k-vertex-connectivity game, played on the edge set of K n, the graph on n vertices. We first study the Maker-Breaker version of this game and prove that, for any integer k ≥ 2 and sufficiently large n, Maker has a strategy to win this game within ⌊k n / 2 ⌋ + 1 moves, which is easily seen to be best possible. This answers a question fromHefetz etal. (2009) [6]. We then consider the strong k-vertex-connectivity game. For every positive integer k and sufficiently large n, we describe an explicit first player's winning strategy for this game.
AB - For a positive integer k, we consider the k-vertex-connectivity game, played on the edge set of K n, the graph on n vertices. We first study the Maker-Breaker version of this game and prove that, for any integer k ≥ 2 and sufficiently large n, Maker has a strategy to win this game within ⌊k n / 2 ⌋ + 1 moves, which is easily seen to be best possible. This answers a question fromHefetz etal. (2009) [6]. We then consider the strong k-vertex-connectivity game. For every positive integer k and sufficiently large n, we describe an explicit first player's winning strategy for this game.
UR - http://www.scopus.com/inward/record.url?scp=84882673664&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2013.06.015
DO - 10.1016/j.ejc.2013.06.015
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84882673664
SN - 0195-6698
VL - 35
SP - 169
EP - 183
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
ER -