Geodesic
The positive minimum degree game on sparse graphs
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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In this note we investigate a special form of degree games defined by D. Hefetz, M. Krivelevich, M. Stojaković and T. Szabó. Usually the board of a graph game is the edge set of $K_n$, 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 $K_n$, Maker first selects as few edges of $K_n$ as possible in order to win, and our goal is to compute the necessary size of that board. Solving a question of Hefetz et al., we show, using the discharging method, that the sharp bound is around $10n/7$ for the positive minimum degree game.
DOI : 10.37236/1174
Classification : 05C57, 05C35, 05C65, 91A43, 91A46
Mots-clés : discharging method 
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     author = {J\'ozsef Balogh and Andr\'as Pluh\'ar},
     title = {The positive minimum degree game on sparse graphs},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/1174},
     zbl = {1243.05163},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1174/}
}
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József Balogh; András Pluhár. The positive minimum degree game on sparse graphs. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/1174

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