We investigate a game played between two players, Maker and Breaker, on a countably infinite complete graph where the vertices are the rational numbers. The players alternately claim unclaimed edges. It is Maker's goal to have after countably many turns a complete infinite graph contained in her coloured edges where the vertex set of the subgraph is order-isomorphic to the rationals. It is Breaker's goal to prevent Maker from achieving this.We prove that there is a winning strategy for Maker in this game. We also prove that there is a winning strategy for Breaker in the game where Maker must additionally make the vertex set of her complete graph dense in the rational numbers.
@article{10_37236_12380,
author = {Nathan Bowler and Florian Gut},
title = {The rational number game},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {4},
doi = {10.37236/12380},
zbl = {1556.05103},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12380/}
}
TY - JOUR
AU - Nathan Bowler
AU - Florian Gut
TI - The rational number game
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/12380/
DO - 10.37236/12380
ID - 10_37236_12380
ER -
%0 Journal Article
%A Nathan Bowler
%A Florian Gut
%T The rational number game
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/12380/
%R 10.37236/12380
%F 10_37236_12380
Nathan Bowler; Florian Gut. The rational number game. The electronic journal of combinatorics, Tome 31 (2024) no. 4. doi: 10.37236/12380
