TY - JOUR
T1 - Biased positional games and small hypergraphs with large covers
AU - Krivelevich, Michael
AU - Szabó, Tibor
PY - 2008/5/5
Y1 - 2008/5/5
N2 - We prove that in the biased (1:6) Hamiltonicity and k-connectivity Maker-Breaker games (k > 0 is a constant), played on the edges of the complete graph Kn, Maker has a winning strategy for 6 ≤ (log 2 - o(1))n/ log n. Also, in the biased (1 : 6) Avoider-Enforcer game played on E(Kn), Enforcer can force Avoider to create a Hamilton cycle when 6 ≤ (1 - o(1))n/ log n. These results are proved using a new approach, relying on the existence of hypergraphs with few edges and large covering number.
AB - We prove that in the biased (1:6) Hamiltonicity and k-connectivity Maker-Breaker games (k > 0 is a constant), played on the edges of the complete graph Kn, Maker has a winning strategy for 6 ≤ (log 2 - o(1))n/ log n. Also, in the biased (1 : 6) Avoider-Enforcer game played on E(Kn), Enforcer can force Avoider to create a Hamilton cycle when 6 ≤ (1 - o(1))n/ log n. These results are proved using a new approach, relying on the existence of hypergraphs with few edges and large covering number.
UR - http://www.scopus.com/inward/record.url?scp=43849095626&partnerID=8YFLogxK
U2 - 10.37236/794
DO - 10.37236/794
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AN - SCOPUS:43849095626
SN - 0022-5282
VL - 15
JO - Electronic Journal of Combinatorics
JF - Electronic Journal of Combinatorics
IS - 1 R
M1 - R70
ER -