Hackenbush
Players hack edges of a graph, deleting substructures that are no longer connected to the ground.
Rules
Board. An undirected graph (loops and multiedges permitted) with a distinguished root vertex (often called the ground). Each edge is labelled with exactly one of the following colours: blue, red, or green.
Left moves. Delete a blue or green edge in the same connected component as .
Right moves. Delete a red or green edge in the same connected component as .
Convention. Classical (normal or misère play).
Notes
Similarly to Partizan Arc Kayles, this ruleset is usually played with the edge colours restricted to blue and red (no green edges). To emphasise this, one might say Blue-Red Hackenbush. When allowing green edges as well, one might say Blue-Red-Green Hackenbush. Also studied is the variant where only green edges are permitted; this is an impartial ruleset called Green Hackenbush.