The decomposability of additive hereditary properties of graphs

• Autorzy: Izak Broere , Michael J. Dorfling
• Języki publikacji: EN

Abstrakty

EN

An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphisms. If 𝓟₁,...,𝓟ₙ are properties of graphs, then a (𝓟₁,...,𝓟ₙ)-decomposition of a graph G is a partition E₁,...,Eₙ of E(G) such that $G[E_i]$, the subgraph of G induced by $E_i$, is in $𝓟_i$, for i = 1,...,n. We define 𝓟₁ ⊕...⊕ 𝓟ₙ as the property {G ∈ 𝓘: G has a (𝓟₁,...,𝓟ₙ)-decomposition}. A property 𝓟 is said to be decomposable if there exist non-trivial hereditary properties 𝓟₁ and 𝓟₂ such that 𝓟 = 𝓟₁⊕ 𝓟₂. We study the decomposability of the well-known properties of graphs 𝓘ₖ, 𝓞ₖ, 𝓦ₖ, 𝓣ₖ, 𝓢ₖ, 𝓓ₖ and $𝓞 ^{p}$.

Słowa kluczowe

EN

property of graphs; additive; hereditary; decomposable property of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2000
• Tom: 20
• Numer: 2
• Strony: 281-291

Daty

wydano

2000

otrzymano

2000-09-05

poprawiono

2000-11-13

Twórcy

autor

Izak Broere

• Department of Mathematics, Faculty of Science, Rand Afrikaans University, P.O. Box 524, Auckland Park, 2006 South Africa

autor

Michael J. Dorfling

• Department of Mathematics, Faculty of Science, Rand Afrikaans University, P.O. Box 524, Auckland Park, 2006 South Africa

Bibliografia

• [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.
• [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.
• [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.
• [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.
• [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
• [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.

Identyfikatory

DOI

10.7151/dmgt.1127