在树上玩加权Tron
Playing weighted Tron on Trees
摘要：
我们考虑图上的Tron游戏的加权版本，其中两个玩家，Alice和Bob，每个人都通过每次声明一个顶点来构建自己的路径，从Alice开始。顶点具有非负权重，总和为1，并且任何一个玩家都试图声称具有比对手更大的总权重的路径。我们表明，如果图是一棵树，那么爱丽丝总是可以确保得到最多1/5小于鲍勃，并存在树，鲍勃可以确保得到至少1/5比爱丽丝。
英文摘要：
We consider the weighted version of the Tron game on graphs where two players, Alice and Bob, each build their own path by claiming one vertex at a time, starting with Alice. The vertices carry non-negative weights that sum up to 1 and either player tries to claim a path with larger total weight than the opponent. We show that if the graph is a tree then Alice can always ensure to get at most 1/5 less than Bob, and that there exist trees where Bob can ensure to get at least 1/5 more than Alice.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
