TY  - JOUR
ID  - Juszczyk2010
LB  - Juszczyk2010
AU  - Juszczyk, Tomasz
AU  - Zioło, Irmina A.
TI  - On some families of arbitrarily vertex decomposable spiders
ST  - On some families of arbitrarily vertex decomposable spiders
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2010
VL  - 30
IS  - 2
SP  - 147
EP  - 154
DO  - http://dx.doi.org/10.7494/OpMath.2010.30.2.147
UR  - http://dx.doi.org/10.7494/OpMath.2010.30.2.147
AB  - 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.
KW  - arbitrarily vertex decomposable graph
KW  - trees
SN  - 1232-9274
ER  -