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## Discussiones Mathematicae Graph Theory

2002 | 22 | 1 | 31-37
Tytuł artykułu

### Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let 𝓟₁,𝓟₂,...,𝓟ₙ be graph properties, a graph G is said to be uniquely (𝓟₁,𝓟₂, ...,𝓟ₙ)-partitionable if there is exactly one (unordered) partition {V₁,V₂,...,Vₙ} of V(G) such that $G[V_i] ∈ 𝓟_i$ for i = 1,2,...,n. We prove that for additive and induced-hereditary properties uniquely (𝓟₁,𝓟₂,...,𝓟ₙ)-partitionable graphs exist if and only if $𝓟_i$ and $𝓟_j$ are either coprime or equal irreducible properties of graphs for every i ≠ j, i,j ∈ {1,2,...,n}.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
31-37
Opis fizyczny
Daty
wydano
2002
otrzymano
2000-08-08
poprawiono
2001-07-02
Twórcy
autor
• Department of Mathematics, Rand Afrikaans University, P.O. Box 524, Auckland Park, 2006 South Africa
autor
• Department of Applied Mathematics, Faculty of Economics, Technical University, B. Nĕmcovej, 040 01 Košice, Slovak Republic
autor
• Department of Applied Mathematics, Faculty of Economics, Technical University, B. Nĕmcovej, 040 01 Košice, Slovak Republic
• Mathematical Institute, Slovak Academy of Science, Gresákova 6, 040 01 Košice, Slovak Republic
Bibliografia
• [1] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, Survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
• [3] I. Broere and J. Bucko, Divisibility in additive hereditary graph properties and uniquely partitionable graphs, Tatra Mt. Math. Publ. 18 (1999) 79-87.
• [4] J. Bucko, M. Frick, P. Mihók and R. Vasky, Uniquely partitionable graphs, Discuss. Math. Graph Theory 17 (1997) 103-114, doi: 10.7151/dmgt.1043.
• [5] F. Harary, S.T. Hedetniemi and R.W. Robinson, Uniquely colourable graphs, J. Combin. Theory 6 (1969) 264-270, doi: 10.1016/S0021-9800(69)80086-4.
• [6] P. Mihók, Additive hereditary properties and uniquely partitionable graphs, in: M. Borowiecki and Z. Skupień, eds., Graphs, hypergraphs and matroids (Zielona Góra, 1985) 49-58.
• [7] P. Mihók, Unique factorization theorem, Discuss. Math. Graph Theory 20 (2000) 143-154, doi: 10.7151/dmgt.1114.
Typ dokumentu
Bibliografia
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