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## Discussiones Mathematicae Graph Theory

1999 | 19 | 2 | 229-236
Tytuł artykułu

### On the completeness of decomposable properties of graphs

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let 𝓟₁,𝓟₂ be additive hereditary properties of graphs. A (𝓟₁,𝓟₂)-decomposition of a graph G is a partition of E(G) into sets E₁, E₂ such that induced subgraph $G[E_i]$ has the property $𝓟_i$, i = 1,2. Let us define a property 𝓟₁⊕𝓟₂ by {G: G has a (𝓟₁,𝓟₂)-decomposition}.
A property D is said to be decomposable if there exists nontrivial additive hereditary properties 𝓟₁, 𝓟₂ such that D = 𝓟₁⊕𝓟₂. In this paper we determine the completeness of some decomposable properties and we characterize the decomposable properties of completeness 2.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
229-236
Opis fizyczny
Daty
wydano
1999
otrzymano
1999-02-12
poprawiono
1999-10-20
Twórcy
autor
• Institute of Mathematics, Technical University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
autor
• Department of Geometry and Algebra, Faculty of Science, P.J. Šafárik University, Jesenná 5, 041 54 Košice, Slovak Republic
Bibliografia
• [1] L.W. Beineke, Decompositions of complete graphs into forests, Magyar Tud. Akad. Mat. Kutato Int. Kozl. 9 (1964) 589-594.
• [2] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
• [3] M. Borowiecki and M. Hałuszczak, Decomposition of some classes of graphs, (manuscript).
• [4] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: V.R. Kulli, ed., Advances in Graph Theory (Vishwa International Publication, Gulbarga, 1991) 41-68.
• [5] S.A. Burr, J.A. Roberts, On Ramsey numbers for stars, Utilitas Math. 4 (1973) 217-220
• [6] G. Chartrand and L. Lesnak, Graphs and Digraphs (Wadsworth & Brooks/Cole, Monterey, California, 1986).
• [7] E.J. Cockayne, Colour classes for r-graphs, Canad. Math. Bull. 15 (1972) 349-354, doi: 10.4153/CMB-1972-063-2.
• [8] P. Mihók Additive hereditary properties and uniquely partitionable graphs, in: M. Borowiecki, Z. Skupień, eds., Graphs, Hypergraphs and Matroids (Zielona Góra, 1985) 49-58.
• [9] P. Mihók and G. Semanišin, Generalized Ramsey Theory and Decomposable Properties of Graphs, (manuscript).
• [10] L. Volkmann, Fundamente der Graphentheorie (Springer, Wien, New York, 1996), doi: 10.1007/978-3-7091-9449-2.
Typ dokumentu
Bibliografia
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