Timeline for Necessary and sufficient conditions for the Cayley graph to be bipartite

12 events

when toggle format	what		by	license	comment
May 14 at 6:06	comment	added	lunch zheng		I get it, by the way, I would like to ask, which book is this theorem from?(The Cayley graph is bipartite)
May 5 at 9:36	comment	added	Corentin B		In order to have a proper coloring, we need $\pi(gs)\ne\pi(g)$ hence $\pi(gs)=\pi(g)+1=\pi(g)+\pi(s)$ for all $g\in G$ and $s\in S$. When the target group is $\mathbb Z/2\mathbb Z$, this is equivalent to $\pi$ being an homomorphism.
May 5 at 8:55	comment	added	lunch zheng		Thank you, and why is it required here that $\pi$ is a homomorphism?
May 5 at 5:07	vote	accept	lunch zheng
May 5 at 5:07	vote	accept	lunch zheng
May 5 at 5:07
May 4 at 14:05	comment	added	Corentin B		@lunch zheng On which topics? Cayley graphs? I guess any book on geometric group theory will cover this (with more or less examples). I guess my favorites are "Offices Hours with Geometric Group Theorist" and "Topics in geometric group theory" (which I legally binded to promote, being in Geneva).
May 4 at 5:46	comment	added	lunch zheng		Thank you for your response. Are there any related books or papers that introduce these topics, especially for specific groups?
May 2 at 16:37	history	edited	Christopher King	CC BY-SA 4.0	added 10 characters in body
May 2 at 10:49	history	edited	Emil Jeřábek	CC BY-SA 4.0	added 11 characters in body
May 2 at 8:15	history	edited	Corentin B	CC BY-SA 4.0	added 6 characters in body
May 2 at 8:09	history	edited	Corentin B	CC BY-SA 4.0	added 110 characters in body
May 2 at 8:07	history	answered	Corentin B	CC BY-SA 4.0