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Component Games on Regular Graphs
Published online by Cambridge University Press: 04 November 2013
Abstract
We study the (1:b) Maker–Breaker component game, played on the edge set of a d-regular graph. Maker's aim in this game is to build a large connected component, while Breaker's aim is to prevent him from doing so. For all values of Breaker's bias b, we determine whether Breaker wins (on any d-regular graph) or Maker wins (on almost every d-regular graph) and provide explicit winning strategies for both players.
To this end, we prove an extension of a theorem of Gallai, Hasse, Roy and Vitaver about graph orientations without long directed simple paths.
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- Copyright © Cambridge University Press 2013
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