Opuscula Mathematica
Opuscula Math. 30, no. 2 (), 147-154
Opuscula Mathematica

On some families of arbitrarily vertex decomposable spiders

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.
Mathematics Subject Classification: 05C05, 05C35.
Cite this article as:
Tomasz Juszczyk, Irmina A. Zioło, On some families of arbitrarily vertex decomposable spiders, Opuscula Math. 30, no. 2 (2010), 147-154, http://dx.doi.org/10.7494/OpMath.2010.30.2.147
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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