Component Games on Regular Graphs
نویسندگان
چکیده
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 not let him do 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 by Gallai–Hasse–Roy–Vitaver about graph orientations without long directed simple paths.
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ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 23 شماره
صفحات -
تاریخ انتشار 2014