TY - JOUR
T1 - Component games on regular graphs
AU - Hod, Rani
AU - Naor, Alon
PY - 2014/1
Y1 - 2014/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84889662262&partnerID=8YFLogxK
U2 - 10.1017/S0963548313000527
DO - 10.1017/S0963548313000527
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AN - SCOPUS:84889662262
SN - 0963-5483
VL - 23
SP - 75
EP - 89
JO - Combinatorics Probability and Computing
JF - Combinatorics Probability and Computing
IS - 1
ER -