@inbook{7229e14a61024d9ab30cafb1f81bee2a,

title = "The Game of Toucher and Isolator",

abstract = "We introduce a new positional game called {\textquoteleft}Toucher-Isolator{\textquoteright}, which is a quantitative version of a Maker-Breaker type game. The playing board is the set of edges of a given graph G, and the two players, Toucher and Isolator, claim edges alternately. The aim of Toucher is to {\textquoteleft}touch{\textquoteright} as many vertices as possible (i.e. to maximise the number of vertices that are incident to at least one of her chosen edges), and the aim of Isolator is to minimise the number of vertices that are so touched. We analyse the number of untouched vertices u(G) at the end of the game when both Toucher and Isolator play optimally, obtaining results both for general graphs and for particularly interesting classes of graphs, such as cycles, paths, trees, and k-regular graphs.",

keywords = "Graphs, Maker-Breaker, Positional games",

author = "Chris Dowden and Mihyun Kang and Mirjana Mikala{\v c}ki and Milo{\v s} Stojakovi{\'c}",

year = "2021",

doi = "10.1007/978-3-030-83823-2_65",

language = "English",

isbn = "978-3-030-83822-5",

series = "Trends in Mathematics",

publisher = "Birkh{\"a}user",

pages = "417--422",

booktitle = "Extended Abstracts EuroComb 2021",

address = "Switzerland",

note = "European Conference on Combinatorics, Graph Theory and Applications : EuroComb 2021 ; Conference date: 06-09-2021 Through 10-09-2021",

}