# On arbitrarily vertex decomposable unicyclic graphs with dominating cycle

Sylwia Cichacz; Irmina A. Zioło

Discussiones Mathematicae Graph Theory (2006)

- Volume: 26, Issue: 3, page 403-412
- ISSN: 2083-5892

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topSylwia Cichacz, and Irmina A. Zioło. "On arbitrarily vertex decomposable unicyclic graphs with dominating cycle." Discussiones Mathematicae Graph Theory 26.3 (2006): 403-412. <http://eudml.org/doc/270726>.

@article{SylwiaCichacz2006,

abstract = {A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n₁,...,nₖ) of positive integers such that $∑^k_\{i=1\} n_i = n$, there exists a partition (V₁,...,Vₖ) of vertex set of G such that for every i ∈ 1,...,k the set $V_i$ induces a connected subgraph of G on $n_i$ vertices. We consider arbitrarily vertex decomposable unicyclic graphs with dominating cycle. We also characterize all such graphs with at most four hanging vertices such that exactly two of them have a common neighbour.},

author = {Sylwia Cichacz, Irmina A. Zioło},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {arbitrarily vertex decomposable graph; dominating cycle},

language = {eng},

number = {3},

pages = {403-412},

title = {On arbitrarily vertex decomposable unicyclic graphs with dominating cycle},

url = {http://eudml.org/doc/270726},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Sylwia Cichacz

AU - Irmina A. Zioło

TI - On arbitrarily vertex decomposable unicyclic graphs with dominating cycle

JO - Discussiones Mathematicae Graph Theory

PY - 2006

VL - 26

IS - 3

SP - 403

EP - 412

AB - A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n₁,...,nₖ) of positive integers such that $∑^k_{i=1} n_i = n$, there exists a partition (V₁,...,Vₖ) of vertex set of G such that for every i ∈ 1,...,k the set $V_i$ induces a connected subgraph of G on $n_i$ vertices. We consider arbitrarily vertex decomposable unicyclic graphs with dominating cycle. We also characterize all such graphs with at most four hanging vertices such that exactly two of them have a common neighbour.

LA - eng

KW - arbitrarily vertex decomposable graph; dominating cycle

UR - http://eudml.org/doc/270726

ER -

## References

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- [2] D. Barth and H. Fournier, A degree bound on decomposable trees, Discrete Math. 306 (2006) 469-477, doi: 10.1016/j.disc.2006.01.006. Zbl1092.05054
- [3] S. Cichacz, A. Görlich, A. Marczyk, J. Przybyło and M. Woźniak, Arbitrarily vertex decomposable caterpillars with four or five leaves, Preprint MD-010 (2005), http://www.ii.uj.edu.pl/preMD/, to appear. Zbl1142.05065
- [4] M. Hornák and M. Woźniak, Arbitrarily vertex decomposable trees are of maximum degree at most six, Opuscula Math. 23 (2003) 49-62. Zbl1093.05510
- [5] R. Kalinowski, M. Pilśniak, M. Woźniak and I.A. Zioło, Arbitrarily vertex decomposable suns with few rays, preprint (2005), http://www.ii.uj.edu.pl/preMD/. Zbl1214.05125
- [6] A. Marczyk, Ore-type condition for arbitrarily vertex decomposable graphs, preprint (2005).

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