Pairs of maximal "almost" disjoint isomorphic subgraphs of spiders - Brigham, Robert C.; Dutton, Ronald D. (Utilitas Mathematica, 1997)
It is possible to partition the vertices of any spider into three sets R, B, and C such that the subgraph induced by R ∪ C is isomorphic to the subgraph induced by B ∪ C and, among all such partitions, |C| is minimum. The quantity |R| = |B| in such a partition is a graphical invariant, and its value is determined for all spiders.