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On cyclically embeddable (n,n)-graphs

100%

Görlich A., Pilśniak M., Woźniak M.

Discussiones Mathematicae Graph Theory

2003

tom 23

nr 1

85-104

An embedding of a simple graph G into its complement G̅ is a permutation σ on V(G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider the embeddable (n,n)-graphs. We prove that with few exceptions the corresponding permutation may be chosen as cyclic one.

Arbitrarily vertex decomposable caterpillars with four or five leaves

88%

Cichacz S., Görlich A., Marczyk A., Przybyło J., Woźniak M.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 2

291-305

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.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Görlich A.

2 Woźniak M.

1 Cichacz S.

1 Marczyk A.

1 Pilśniak M.

1 Przybyło J.

1 2006

1 2003

Wyniki wyszukiwania

On cyclically embeddable (n,n)-graphs

Arbitrarily vertex decomposable caterpillars with four or five leaves