Figure 8

Illustration of admissible and non-admissible pairs. A cycle will be created by adding each edge shown by a black dotted line. Two 1-augmented trees T+u v and T+u v^′ are 1-augmented trees obtained from the multi-tree T by adding a simple edge such that T+u v and T+u v^′ are isomorphic to each other. (a) The vertex pair (u,v) is an admissible pair, and (b) the other is not an admissible pair (at least one admissible pair always exists in every 1-augmented tree). Therefore, T+u v^′ is not created (all 1-augmented trees are discarded except for the 1-augmented tree created for admissible pair).