The Positive Minimum Degree Game on Sparse Graphs
نویسندگان
چکیده
In this note we investigate a special form of degree games defined by D. Hefetz, M. Krivelevich, M. Stojaković and T. Szabó [4]. Usually the board of a graph game is the edge set of Kn, the complete graph on n vertices. Maker and Breaker alternately claim an edge, and Maker wins if his edges form a subgraph with prescribed properties; here a certain minimum degree. In the special form the board is no longer the whole edge set of Kn, Maker first selects as few edges of Kn as possible in order to win, and our goal is to compute the necessary size of that board. Solving a question of [4], we show, using the discharging method, that the sharp bound is around 10n/7 for the positive minimum degree game.
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عنوان ژورنال:
- Electr. J. Comb.
دوره 19 شماره
صفحات -
تاریخ انتشار 2012