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## Discussiones Mathematicae Graph Theory

2006 | 26 | 2 | 291-305
Tytuł artykułu

### Arbitrarily vertex decomposable caterpillars with four or five leaves

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A graph G of order n is called arbitrarily vertex decomposable if for each sequence (a₁,...,aₖ) of positive integers such that a₁+...+aₖ = n there exists a partition (V₁,...,Vₖ) of the vertex set of G such that for each i ∈ {1,...,k}, $V_i$ induces a connected subgraph of G on $a_i$ vertices. D. Barth and H. Fournier showed that if a tree T is arbitrarily vertex decomposable, then T has maximum degree at most 4. In this paper we give a complete characterization of arbitrarily vertex decomposable caterpillars with four leaves. We also describe two families of arbitrarily vertex decomposable trees with maximum degree three or four.
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EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
291-305
Opis fizyczny
Daty
wydano
2006
otrzymano
2005-01-26
poprawiono
2005-10-05
Twórcy
autor
• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
autor
• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
autor
• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
autor
• Faculty of Applied Mathematics, AGH University of Science and Technology, Al. Mickiewicza 30, 30-059 Kraków, Poland
autor
• Institute of Mathematics of Polish Academy of Sciences
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] M. Hornák and M. Woźniak, On arbitrarily vertex decomposable trees, Technical report, Faculty of Applied Mathematics, Kraków (2003), submitted.
• [4] M. Hornák and M. Woźniak, Arbitrarily vertex decomposable trees are of maximum degree at most six, Opuscula Mathematica 23 (2003) 49-62.
Typ dokumentu
Bibliografia
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