@Article{Juszczyk2010,
author = "Juszczyk, Tomasz and Zioło, Irmina A.",
title = "On some families of arbitrarily vertex decomposable spiders",
journal = "Opuscula Math.",
year = "2010",
volume = "30",
number = "2",
pages = "147--154",
doi = "http://dx.doi.org/10.7494/OpMath.2010.30.2.147",
url = "http://dx.doi.org/10.7494/OpMath.2010.30.2.147",
abstract = "A graph \(G\) of order \(n\) is called arbitrarily vertex decomposable if for each sequence \((n_1, ..., n_k)\) of positive integers such that \(\sum _{i=1}^{k} n_i = n\), there exists a partition \((V_1, ..., V_k)\) of the vertex set of \(G\) such that for every \(i \in \{1, ...., k\}\) the set \(V_i\) induces a connected subgraph of \(G\) on \(n_i\) 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.",
keywords = "arbitrarily vertex decomposable graph, trees",
issn = "1232-9274"
}