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.

Full text (pdf)

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

a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.