On the lattice of additive hereditary properties of finite graphs

• Autorzy: Ján Jakubík
• Języki publikacji: EN

Abstrakty

EN

In this paper it is proved that the lattice of additive hereditary properties of finite graphs is completely distributive and that it does not satisfy the Jordan-Dedekind condition for infinite chains.

Słowa kluczowe

EN

Lattice; complete distributivity; finite graph; additive hereditary property; generalized Jordan-Dedekind condition

Kategorie tematyczne

• 06D10: Complete distributivity
• 05C99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2002
• Tom: 22
• Numer: 1
• Strony: 73-86

Daty

wydano

2002

otrzymano

2002-02-28

Twórcy

autor

Ján Jakubík

• Matemathical Institute, Slovak Academy of Sciences, Grešákova 6, 040-01 Košice, Slovakia

Bibliografia

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• [3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, 'Advances in Graph Theory', Vishwa International Publications, Gulbarga 1991, 41-68.
• [4] G. Grätzer and E. T. Schmidt, On the Jordan-Dedekind chain condition, Acta Sci. Math. 18 (1957), 52-56.
• [5] J. Jakubík, On the Jordan-Dedekind chain condition, Acta Sci. Math. 16 (1955), 266-269.
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• [8] J. Jakubí k, Die Jordan-Dedekindsche Bedingung im direkten Produkt von geordneten Mengen, Acta Sci. Math. 24 (1963), 20-23.
• [9] P. Mihók, On graphs critical with respect to generalized independence numbers, Colloq. Math. Soc. J. Bolyai 52 (1987), 417-421.
• [10] G.N. Raney, Completely distributive complete lattices, Proc. Amer. Math. Soc. 3 (1952), 677-680.
• [11] G.N. Raney, A subdirect-union representation for completely distributive lattices, Proc. Amer. Math. Soc. 4 (1952), 518-522.
• [12] G.N. Raney, Tight Galois connection and complete distributivity, Trans. Amer. Math. Soc. 97 (1960), 418-426.
• [13] R. Sikorski, Boolean Algebras (the second edition), Springer-Verlag, Berlin 1964.
• [14] G. Szász, Generalization of a theorem of Birkhoff concerning maximal chains of a certain type of lattices, Acta Sci. Math. 16 (1955), 89-91.

Identyfikatory

DOI

10.7151/dmgaa.1048