On the lattice of additive hereditary properties of finite graphs

Ján Jakubík

Discussiones Mathematicae - General Algebra and Applications (2002)

  • Volume: 22, Issue: 1, page 73-86
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Ján Jakubík. "On the lattice of additive hereditary properties of finite graphs." Discussiones Mathematicae - General Algebra and Applications 22.1 (2002): 73-86. <http://eudml.org/doc/287681>.

@article{JánJakubík2002,
abstract = {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.},
author = {Ján Jakubík},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {Lattice; complete distributivity; finite graph; additive hereditary property; generalized Jordan-Dedekind condition; completely distributive lattice},
language = {eng},
number = {1},
pages = {73-86},
title = {On the lattice of additive hereditary properties of finite graphs},
url = {http://eudml.org/doc/287681},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Ján Jakubík
TI - On the lattice of additive hereditary properties of finite graphs
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2002
VL - 22
IS - 1
SP - 73
EP - 86
AB - 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.
LA - eng
KW - Lattice; complete distributivity; finite graph; additive hereditary property; generalized Jordan-Dedekind condition; completely distributive lattice
UR - http://eudml.org/doc/287681
ER -

References

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  1. [1] G. Birkhoff, Lattice Theory, (the 3-rd ed.), Amer. Math. Soc., Providence, RI, 1967. 
  2. [2] M. Borowiecki, I. Broere, M. Frick, P. Mihók, and G. Semanisin, A survey of hereditary properties of graphs, Discussiones Math.- Graph Theory 17 (1997), 5-50. Zbl0902.05026
  3. [3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, 'Advances in Graph Theory', Vishwa International Publications, Gulbarga 1991, 41-68. 
  4. [4] G. Grätzer and E. T. Schmidt, On the Jordan-Dedekind chain condition, Acta Sci. Math. 18 (1957), 52-56. Zbl0079.04501
  5. [5] J. Jakubík, On the Jordan-Dedekind chain condition, Acta Sci. Math. 16 (1955), 266-269. Zbl0065.26602
  6. [6] J. Jakubík, A remark on the Jordan-Dedekind chain condition in Boolean algebras (Slovak), Casopis Pest. Mat. 82 (1957), 44-46. 
  7. [7] J. Jakubík, On chains in Boolean algebras (Slovak), Mat. Fyz. Casopis SAV 8 (1958), 193-202. Zbl0086.25302
  8. [8] J. Jakubí k, Die Jordan-Dedekindsche Bedingung im direkten Produkt von geordneten Mengen, Acta Sci. Math. 24 (1963), 20-23. Zbl0118.02203
  9. [9] P. Mihók, On graphs critical with respect to generalized independence numbers, Colloq. Math. Soc. J. Bolyai 52 (1987), 417-421. 
  10. [10] G.N. Raney, Completely distributive complete lattices, Proc. Amer. Math. Soc. 3 (1952), 677-680. Zbl0049.30304
  11. [11] G.N. Raney, A subdirect-union representation for completely distributive lattices, Proc. Amer. Math. Soc. 4 (1952), 518-522. Zbl0053.35201
  12. [12] G.N. Raney, Tight Galois connection and complete distributivity, Trans. Amer. Math. Soc. 97 (1960), 418-426. Zbl0098.02703
  13. [13] R. Sikorski, Boolean Algebras (the second edition), Springer-Verlag, Berlin 1964. 
  14. [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. Zbl0064.02904

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