Reducible properties of graphs

• Autorzy: P. Mihók , G. Semanišin
• Języki publikacji: EN

Abstrakty

EN

Let L be the set of all hereditary and additive properties of graphs. For P₁, P₂ ∈ L, the reducible property R = P₁∘P₂ is defined as follows: G ∈ R if and only if there is a partition V(G) = V₁∪ V₂ of the vertex set of G such that $⟨V₁⟩_G ∈ P₁$ and $⟨V₂⟩_G ∈ P₂$. The aim of this paper is to investigate the structure of the reducible properties of graphs with emphasis on the uniqueness of the decomposition of a reducible property into irreducible ones.

Słowa kluczowe

EN

hereditary property of graphs; additivity; reducibility

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1995
• Tom: 15
• Numer: 1
• Strony: 11-18

Daty

wydano

1995

otrzymano

1994-01-20

poprawiono

1994-11-15

Twórcy

autor

P. Mihók

• Department of Geometry and Algebra, Faculty of Sciences, P. J. Šafárik's University, Jesenná 5, 04154 Košice, Slovak Republic

autor

G. Semanišin

• Department of Geometry and Algebra, Faculty of Sciences, P. J. Šafárik's University, Jesenná 5, 04154 Košice, Slovak Republic

Bibliografia

• [1] V. E. Alekseev, Range of values of entropy of hereditary classes of graphs, Diskretnaja matematika 4 (1992) 148-157 (Russian).
• [2] M. Borowiecki, P. Mihók, Hereditary properties of graphs in: Advances in Graph Theory, Vishwa International Publication, India, (1991) 42-69.
• [3] G. Chartrand, L. Lesniak, Graphs and Digraphs (Wadsworth & Brooks/Cole, Monterey California 1986).
• [4] P. Mihók, Additive hereditary properties and uniquely partitionable graphs, in: Graphs, Hypergraphs and Matroids (Zielona Góra, 1985) 49-58.
• [5] P. Mihók, An extension of Brook's theorem, Annals of Discrete Math. 51 (1992) 235-236.
• [6] P. Mihók, On the minimal reducible bound for outerplanar and planar graphs, (to appear).
• [7] M. Simonovits, Extremal graph theory, in: L. W. Beineke and R. J. Wilson eds. Selected Topics in Graph Theory 2 (Academic Press, London, 1983) 161-200.
• [8] E. R. Scheinerman, On the structure of hereditary classes of graphs, Journal of Graph Theory 10 (1986) 545-551, doi: 10.1002/jgt.3190100414.
• [9] E. R. Scheinerman, J. Zito, On the size of hereditary classes of graphs, J. Combin. Theory (B) 61 (1994) 16-39, doi: 10.1006/jctb.1994.1027.

Identyfikatory

DOI

10.7151/dmgt.1002