Opuscula Math. 30, no. 2 (2010), 147-154
http://dx.doi.org/10.7494/OpMath.2010.30.2.147

 
Opuscula Mathematica

On some families of arbitrarily vertex decomposable spiders

Tomasz Juszczyk
Irmina A. Zioło

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.

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  • Tomasz Juszczyk
  • AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics, Computer Science and Electronics, al. Mickiewicza 30, 30-059 Kraków, Poland
  • Irmina A. Zioło
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland
  • Received: 2007-10-10.
  • Revised: 2009-11-18.
  • Accepted: 2010-01-04.
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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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