1Institut f\"{u}r Mathematik, Technische Universit\"{a}t Hamburg-Harburg, Germany 2Department for Mathematics and Informatics, University of Novi Sad, Serbia
The electronic journal of combinatorics, Tome 22 (2015) no. 3
We study the Maker-Breaker tournament game played on the edge set of a given graph $G$. Two players, Maker and Breaker, claim unclaimed edges of $G$ in turns, while Maker additionally assigns orientations to the edges that she claims. If by the end of the game Maker claims all the edges of a pre-defined goal tournament, she wins the game. Given a tournament $T_k$ on $k$ vertices, we determine the threshold bias for the $(1:b)$$T_k$-tournament game on $K_n$. We also look at the $(1:1)$$T_k$-tournament game played on the edge set of a random graph ${\mathcal{G}_{n,p}}$ and determine the threshold probability for Maker's win. We compare these games with the clique game and discuss whether a random graph intuition is satisfied.
1
Institut f\"{u}r Mathematik, Technische Universit\"{a}t Hamburg-Harburg, Germany
2
Department for Mathematics and Informatics, University of Novi Sad, Serbia
@article{10_37236_5142,
author = {Dennis Clemens and Mirjana Mikala\v{c}ki},
title = {A remark on the tournament game},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {3},
doi = {10.37236/5142},
zbl = {1323.05089},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5142/}
}
TY - JOUR
AU - Dennis Clemens
AU - Mirjana Mikalački
TI - A remark on the tournament game
JO - The electronic journal of combinatorics
PY - 2015
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UR - http://geodesic.mathdoc.fr/articles/10.37236/5142/
DO - 10.37236/5142
ID - 10_37236_5142
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%A Dennis Clemens
%A Mirjana Mikalački
%T A remark on the tournament game
%J The electronic journal of combinatorics
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%U http://geodesic.mathdoc.fr/articles/10.37236/5142/
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Dennis Clemens; Mirjana Mikalački. A remark on the tournament game. The electronic journal of combinatorics, Tome 22 (2015) no. 3. doi: 10.37236/5142
