Discussiones Mathematicae Graph Theory 15(1) (1995)
11-18
DOI: https://doi.org/10.7151/dmgt.1002
REDUCIBLE PROPERTIES OF GRAPHS
P. Mihók and G. Semanišin
Department of Geometry and Algebra, Faculty of
Sciences,
P. J. Šafárik's University
Jesenná 5, 04154 Košice, Slovak Republic
Abstract
Let L be the set of all hereditary and additive properties of graphs. For P1, P2 ∈L, the reducible property R = P1ºP2 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
1991 Mathematics Subject Classification: 05C15, 05C75
References
[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. |
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