Building Spanning Trees Quickly in Maker-Breaker Games
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Clemens-2015-Building spanning.pdf
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314.77 KB
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Checksum (MD5)
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Author(s)
Clemens, Dennis
Ferber, Asaf
Glebov, Roman
Hefetz, Dan
Liebenau, Anita
Date Issued
September 2015
Journal
SIAM Journal on Discrete Mathematics
Publisher
Society for Industrial and Applied Mathematics
Citation
Clemens, Dennis, Asaf Ferber, Roman Glebov, Dan Hefetz, and Anita Liebenau. “Building Spanning Trees Quickly in Maker-Breaker Games.” SIAM Journal on Discrete Mathematics 29, no. 3 (January 2015): 1683–1705. © 2015, Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
For a tree T on n vertices, we study the Maker-Breaker game, played on the edge set of the complete graph on n vertices, which Maker wins as soon as the graph she builds contains a copy of T. We prove that if T has bounded maximum degree and $n$ is sufficiently large, then Maker can win this game within n+1 moves. Moreover, we prove that Maker can build almost every tree on n vertices in n-1 moves and provide nontrivial examples of families of trees which Maker cannot build in n-1 moves.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/140976054
