On arbitrarily vertex decomposable unicyclic graphs with dominating cycle

• Autorzy: Sylwia Cichacz , Irmina A. Zioło
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

arbitrarily vertex decomposable graph; dominating cycle

Kategorie tematyczne

• 05C35: Extremal problems
• 05C38: Paths and cycles
• 05C99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2006
• Tom: 26
• Numer: 3
• Strony: 403-412

Daty

wydano

2006

otrzymano

2005-11-30

poprawiono

2006-03-31

Twórcy

autor

Sylwia Cichacz

• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. A. Mickiewicza 30, 30-059 Kraków, Poland

autor

Irmina A. Zioło

• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. A. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

• [1] D. Barth, O. Baudon and J. Puech, Decomposable trees: a polynomial algorithm for tripodes, Discrete Appl. Math. 119 (2002) 205-216, doi: 10.1016/S0166-218X(00)00322-X.
• [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.
• [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.
• [4] M. Hornák and M. Woźniak, Arbitrarily vertex decomposable trees are of maximum degree at most six, Opuscula Math. 23 (2003) 49-62.
• [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/.
• [6] A. Marczyk, Ore-type condition for arbitrarily vertex decomposable graphs, preprint (2005).

Identyfikatory

DOI

10.7151/dmgt.1332