The decomposability of additive hereditary properties of graphs
Izak Broere ; Michael J. Dorfling
Discussiones Mathematicae Graph Theory, Tome 20 (2000), p. 281-291 / Harvested from The Polish Digital Mathematics Library
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An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If ₁,...,ₙ are properties of graphs, then a (₁,...,ₙ)-decomposition of a graph G is a partition E₁,...,Eₙ of E(G) such that G[Ei], the subgraph of G induced by Ei, is in i, for i = 1,...,n. We define ₁ ⊕...⊕ ₙ as the property G ∈ : G has a (₁,...,ₙ)-decomposition. A property is said to be decomposable if there exist non-trivial hereditary properties ₁ and ₂ such that = ₁⊕ ₂. We study the decomposability of the well-known properties of graphs ₖ, ₖ, ₖ, ₖ, ₖ, ₖ and p.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:270686 
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Izak Broere; Michael J. Dorfling. The decomposability of additive hereditary properties of graphs. Discussiones Mathematicae Graph Theory, Tome 20 (2000) pp. 281-291. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1127/

[000] [1] M. Borowiecki and M. Hałuszczak, Decompositions of some classes of graphs, Report No. IM-3-99, Institute of Mathematics, Technical University of Zielona Góra, 1999. | Zbl 0905.05061

[001] [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. | Zbl 0902.05026

[002] [3] S.A. Burr, M.S. Jacobson, P. Mihók and G. Semanišin, Generalized Ramsey theory and decomposable properties of graphs, Discuss. Math. Graph Theory 19 (1999) 199-217, doi: 10.7151/dmgt.1095. | Zbl 0958.05094

[003] [4] M. Hałuszczak and P. Vateha, On the completeness of decomposable properties of graphs, Discuss. Math. Graph Theory 19 (1999) 229-236, doi: 10.7151/dmgt.1097.

[004] [5] P. Mihók, G. Semanišin and R. Vasky, Additive and hereditary properties of graphs are uniquely factorizable into irreducible factors, J. Graph Theory 33 (2000) 44-53, doi: 10.1002/(SICI)1097-0118(200001)33:1<44::AID-JGT5>3.0.CO;2-O | Zbl 0942.05056

[005] [6] J. Nesetril and V. Rödl, Simple proof of the existence of restricted Ramsey graphs by means of a partite construction, Combinatorica 1 (1981) 199-202, doi: 10.1007/BF02579274. | Zbl 0491.05044