TUHH Open Research
Help
  • Log In
    New user? Click here to register.Have you forgotten your password?
  • English
  • Deutsch
  • Communities & Collections
  • Publications
  • Research Data
  • People
  • Institutions
  • Projects
  • Statistics
  1. Home
  2. TUHH
  3. Publication References
  4. The Random Graph Intuition for the Tournament Game
 
Options

The Random Graph Intuition for the Tournament Game

Publikationstyp
Journal Article
Date Issued
2016-01-01
Sprache
English
Author(s)
Clemens, Dennis  orcid-logo
Gebauer, Heidi  
Liebenau, Anita  
Institut
Mathematik E-10  
TORE-URI
http://hdl.handle.net/11420/5950
Journal
Combinatorics, probability & computing  
Volume
25
Issue
1
Start Page
76
End Page
88
Citation
Combinatorics Probability and Computing 1 (25): 76-88 (2016-01-01)
Publisher DOI
10.1017/S096354831500019X
Scopus ID
2-s2.0-84952980018
In the tournament game two players, called Maker and Breaker, alternately take turns in claiming an unclaimed edge of the complete graph Kn and selecting one of the two possible orientations. Before the game starts, Breaker fixes an arbitrary tournament Tk on k vertices. Maker wins if, at the end of the game, her digraph contains a copy of Tk; otherwise Breaker wins. In our main result, we show that Maker has a winning strategy for k = (2-o(1))log2 n, improving the constant factor in previous results of Beck and the second author. This is asymptotically tight since it is known that for k = (2-o(1))log2 n Breaker can prevent the underlying graph of Maker's digraph from containing a k-clique. Moreover, the precise value of our lower bound differs from the upper bound only by an additive constant of 12. We also discuss the question of whether the random graph intuition, which suggests that the threshold for k is asymptotically the same for the game played by two 'clever' players and the game played by two 'random' players, is supported by the tournament game. It will turn out that, while a straightforward application of this intuition fails, a more subtle version of it is still valid. Finally, we consider the orientation game version of the tournament game, where Maker wins the game if the final digraph-also containing the edges directed by Breaker-possesses a copy of Tk. We prove that in that game Breaker has a winning strategy for k = (4 + o(1))log2 n.
TUHH
Weiterführende Links
  • Contact
  • Send Feedback
  • Cookie settings
  • Privacy policy
  • Impress
DSpace Software

Built with DSpace-CRIS software - Extension maintained and optimized by 4Science
Design by effective webwork GmbH

  • Deutsche NationalbibliothekDeutsche Nationalbibliothek
  • ORCiD Member OrganizationORCiD Member Organization
  • DataCiteDataCite
  • Re3DataRe3Data
  • OpenDOAROpenDOAR
  • OpenAireOpenAire
  • BASE Bielefeld Academic Search EngineBASE Bielefeld Academic Search Engine
Feedback