TITLE: Who colored in my Dynkin diagrams?
QUESTION [12 upvotes]: Many of you will recognize these as the ADE diagrams, festively colored for the holidays!
     (source)


Does anyone know a mathematical interpretation for these diagrams, when colored like this?


Edit: the answers below seem to treat the set of red nodes and the set of green nodes as essentially equivalent.  However in the combinatorics relevant to me, the red and green ones play slightly different roles; does this also happen in the Coxeter group story?

REPLY [3 votes]: The fact that Dynkin diagrams are bipartite allows one to define the box product $X\square Y$ of two Dynkin diagrams (or rather, of two quivers whose underlying graphs are Dynkin diagrams). This is very relevant in the study of Zamolodchikov perodicity; see e.g. https://arxiv.org/abs/1001.1531 and https://arxiv.org/abs/1506.05378.