Abstract
We present a general approach connecting biased Maker-Breaker games and problems about local resilience in random graphs. We utilize this approach to prove new results and also to derive some known results about biased Maker-Breaker games. In particular, we show that for b=o(n), Maker can build a pancyclic graph (that is, a graph that contains cycles of every possible length) while playing a (1:b) game on E(Kn). As another application, we show that for b=Θ(n/lnn), playing a (1:b) game on E(Kn), Maker can build a graph which contains copies of all spanning trees having maximum degree Δ=O(1) with a bare path of linear length (a bare path in a tree T is a path with all interior vertices of degree exactly two in T).
Original language | English (US) |
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Pages (from-to) | 615-634 |
Number of pages | 20 |
Journal | Random Structures and Algorithms |
Volume | 47 |
Issue number | 4 |
DOIs | |
State | Published - Dec 2015 |
Bibliographical note
Publisher Copyright:© 2015 Wiley Periodicals, Inc.
Keywords
- Games
- Random Graphs