Geodesic
Reducible properties of graphs
Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 11-18.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: hereditary property of graphs, additivity, reducibility 
@article{DMGT_1995_15_1_a1,
     author = {Mih\'ok, P. and Semani\v{s}in, G.},
     title = {Reducible properties of graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {11--18},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_1995_15_1_a1/}
}
TY  - JOUR
AU  - Mihók, P.
AU  - Semanišin, G.
TI  - Reducible properties of graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 1995
SP  - 11
EP  - 18
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_1995_15_1_a1/
LA  - en
ID  - DMGT_1995_15_1_a1
ER  - 
%0 Journal Article
%A Mihók, P.
%A Semanišin, G.
%T Reducible properties of graphs
%J Discussiones Mathematicae. Graph Theory
%D 1995
%P 11-18
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_1995_15_1_a1/
%G en
%F DMGT_1995_15_1_a1
Mihók, P.; Semanišin, G. Reducible properties of graphs. Discussiones Mathematicae. Graph Theory, Tome 15 (1995) no. 1, pp. 11-18. http://geodesic.mathdoc.fr/item/DMGT_1995_15_1_a1/

[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.