On some families of arbitrarily vertex decomposable spiders
Tomasz Juszczyk, Irmina A. Zioło · Opuscula Mathematica · 2010
A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n1, . . ., n k ) of positive integers such that P k i=1 ni = n, there exists a partition (V1, . . ., V k ) of the vertex set of G such that for every i ∈ {1, . . ., k} the set Vi induces a connected subgraph of G on ni vertices.A spider is a tree with one vertex of degree at least 3.We characterize two families of arbitrarily vertex decomposable spiders which are homeomorphic to stars with at most four hanging edges.