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2003 | 23 | 1 | 117-127
Tytuł artykułu

Prime ideals in the lattice of additive induced-hereditary graph properties

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
An additive induced-hereditary property of graphs is any class of finite simple graphs which is closed under isomorphisms, disjoint unions and induced subgraphs. The set of all additive induced-hereditary properties of graphs, partially ordered by set inclusion, forms a completely distributive lattice. We introduce the notion of the join-decomposability number of a property and then we prove that the prime ideals of the lattice of all additive induced-hereditary properties are divided into two groups, determined either by a set of excluded join-irreducible properties or determined by a set of excluded properties with infinite join-decomposability number. We provide non-trivial examples of each type.
Wydawca
Rocznik
Tom
23
Numer
1
Strony
117-127
Opis fizyczny
Daty
wydano
2003
otrzymano
2001-07-12
poprawiono
2002-07-29
Twórcy
  • Department of Mathematics, Rand Afrikaans University, P.O. Box 524, Auckland Park, 2006 South Africa
autor
  • Departement of Applied Mathematics and Informatics, Faculty of Economics, University of Technology, B. Nĕmcovej 32, 040 02 Košice, Slovakia
  • Mathematical Institute of Slovak Academy of Sciences, Gresákova 6, 040 01 Košice, Slovakia
Bibliografia
  • [1] A. Berger, I. Broere, P. Mihók and S. Moagi, Meet- and join-irreducibility of additive hereditary properties of graphs, Discrete Math. 251 (2002) 11-18, doi: 10.1016/S0012-365X(01)00323-5.
  • [2] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, Survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037.
  • [3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: V.R. Kulli, ed., Advances in Graph Theory (Vishwa International Publication, Gulbarga, 1991) 41-68.
  • [4] G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove and D.S. Scott, A Compendium of Continuous Lattices (Springer-Verlag, 1980).
  • [5] G. Grätzer, General Lattice Theory (Second edition, Birkhäuser Verlag, Basel, Boston, Berlin 1998).
  • [6] J. Jakubík, On the lattice of additive hereditary properties of finite graphs, Discuss. Math. General Algebra and Applications 22 (2002) 73-86.
  • [7] T.R. Jensen and B. Toft, Graph Colouring Problems (Wiley-Interscience Publications, New York, 1995).
  • [8] E.R. Scheinerman, Characterizing intersection classes of graphs, Discrete Math. 55 (1985) 185-193, doi: 10.1016/0012-365X(85)90047-0.
  • [9] E.R. Scheinerman, On the structure of hereditary classes of graphs, J. Graph Theory 10 (1986) 545-551.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1189
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