(a) G (b) Three embedded trees (c) Genetic flow The dotted horizontal lines represent time (in generation) and the extant samples, numbered 1, 2, 3, are at the bottom row. Thus K = 3, in this example. The genetic material flows from the nodes at a higher level to the nodes at the lower level in the figures. The hatched nodes are the genetic exchange nodes. (a) The topology of an instance of an ARG, where the GMRCA is marked by an additional ring. (b) A possible embedding of (a) by 3 trees (shown in red, green and blue respectively) by Thm (1). (c) Genetic event labels on the ARG.