论文标题
在树木和周期的爆破上抓住图形游戏
The graph grabbing game on blow-ups of trees and cycles
论文作者
论文摘要
Alice and Bob在非接管性的连接图上进行了图形抓游戏，他们交替声称Alice首先播放了剩下的图表，以最大程度地提高游戏结尾处的权重，以最大程度地提高游戏结尾的权重。 Seacrest和Seacrest猜想，爱丽丝可以保护每个加权连接的两分甚至图的重量的一半。后来，Egawa，Inomoto和Matsumoto部分证实了这一猜想，表明Alice在一类加权连接的双分部分上赢得了游戏，甚至称为$ K_ {M，N} $ -TROED。我们将此类的结果扩展到包括许多图形，例如甚至树木和周期的爆炸。
The graph grabbing game is played on a non-negatively weighted connected graph by Alice and Bob who alternately claim a non-cut vertex from the remaining graph, where Alice plays first, to maximize the weights on their respective claimed vertices at the end of the game when all vertices have been claimed. Seacrest and Seacrest conjectured that Alice can secure at least half of the weight of every weighted connected bipartite even graph. Later, Egawa, Enomoto and Matsumoto partially confirmed this conjecture by showing that Alice wins the game on a class of weighted connected bipartite even graphs called $K_{m,n}$-trees. We extend the result on this class to include a number of graphs, e.g. even blow-ups of trees and cycles.
