TY - JOUR
T1 - Biased orientation games
AU - Ben-Eliezer, Ido
AU - Krivelevich, Michael
AU - Sudakov, Benny
N1 - Funding Information:
The first author’s research was supported in part by an ERC advanced grant and by Dan David fellowship. The second author’s research was supported in part by USA-Israel BSF grant 2006322 , and by grant 1063/08 from the Israel Science Foundation . The third author’s research was supported in part by NSF grant DMS-1101185 , NSF CAREER award DMS-0812005 and by USA-Israeli BSF grant.
PY - 2012/5/28
Y1 - 2012/5/28
N2 - We study biased orientation games, in which the board is the complete graph K n, and OMaker (oriented maker) and OBreaker (oriented breaker) take turns in directing previously undirected edges of K n. At the end of the game, the obtained graph is a tournament. OMaker wins if the tournament has some property P and OBreaker wins otherwise. We provide bounds on the bias that is required for OMaker's win and for OBreaker's win in three different games. In the first game OMaker wins if the obtained tournament has a cycle. The second game is Hamiltonicity, where OMaker wins if the obtained tournament contains a Hamilton cycle. Finally, we consider the H-creation game, where OMaker wins if the obtained tournament has a copy of some fixed digraph H.
AB - We study biased orientation games, in which the board is the complete graph K n, and OMaker (oriented maker) and OBreaker (oriented breaker) take turns in directing previously undirected edges of K n. At the end of the game, the obtained graph is a tournament. OMaker wins if the tournament has some property P and OBreaker wins otherwise. We provide bounds on the bias that is required for OMaker's win and for OBreaker's win in three different games. In the first game OMaker wins if the obtained tournament has a cycle. The second game is Hamiltonicity, where OMaker wins if the obtained tournament contains a Hamilton cycle. Finally, we consider the H-creation game, where OMaker wins if the obtained tournament has a copy of some fixed digraph H.
KW - Directed graphs
KW - Hamiltonicity
KW - Orientation games
UR - http://www.scopus.com/inward/record.url?scp=84858797927&partnerID=8YFLogxK
U2 - 10.1016/j.disc.2012.01.026
DO - 10.1016/j.disc.2012.01.026
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AN - SCOPUS:84858797927
SN - 0012-365X
VL - 312
SP - 1732
EP - 1742
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 10
ER -