Component Games on Regular Graphs
Keyword(s):
We study the (1:b) Maker–Breaker component game, played on the edge set of ad-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 biasb, we determine whether Breaker wins (on anyd-regular graph) or Maker wins (on almost everyd-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.
Keyword(s):
1966 ◽
Vol 18
◽
pp. 1091-1094
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1986 ◽
Vol 41
(2)
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pp. 193-210
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Keyword(s):
1967 ◽
Vol 19
◽
pp. 644-648
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2000 ◽
Vol 9
(3)
◽
pp. 241-263
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2010 ◽
Vol 02
(04)
◽
pp. 643-654
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