The Game of Toucher and Isolator

Chris Dowden, Mihyun Kang, Mirjana Mikalački*, Miloš Stojaković

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


We introduce a new positional game called ‘Toucher-Isolator’, 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 ‘touch’ 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.

Original languageEnglish
Title of host publicationExtended Abstracts EuroComb 2021
Subtitle of host publicationEuropean Conference on Combinatorics, Graph Theory and Applications
Place of PublicationCham
Number of pages6
ISBN (Electronic)978-3-030-83823-2
ISBN (Print)978-3-030-83822-5
Publication statusPublished - 2021
EventEuropean Conference on Combinatorics, Graph Theory and Applications: EuroComb 2021 - Online, Virtual, Barcelona, Spain
Duration: 6 Sep 202110 Sep 2021

Publication series

NameTrends in Mathematics
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X


ConferenceEuropean Conference on Combinatorics, Graph Theory and Applications
CityVirtual, Barcelona


  • Graphs
  • Maker-Breaker
  • Positional games

ASJC Scopus subject areas

  • Mathematics(all)


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