Graph grabbing games and toucher-isolator games

Abstract

In this research, we study the graph grabbing game and the Toucher-Isolator game. In the graph grabbing game, we partially confirm a conjecture of Seacrest and Seacrest which states that Alice wins the game on every weighted connected bipartite even graph. In the Toucher-Isolator game, we give a simple alternative proof of a result of Räty that determines the most suitable tree on n vertices for Toucher which answers a question of Dowden, Kang, Mikalački and Stojaković.