A note on joins of additive hereditary graph properties

Ewa Drgas-Burchardt

Discussiones Mathematicae Graph Theory (2006)

  • Volume: 26, Issue: 3, page 413-418
  • ISSN: 2083-5892

Abstract

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Let L a denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set ( L a , ⊆ ) is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in ( L a , ⊆ ) has a finite or infinite family of minimal forbidden subgraphs.

How to cite

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Ewa Drgas-Burchardt. "A note on joins of additive hereditary graph properties." Discussiones Mathematicae Graph Theory 26.3 (2006): 413-418. <http://eudml.org/doc/270690>.

@article{EwaDrgas2006,
abstract = {Let $L^a$ denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set $(L^a, ⊆ )$ is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in $(L^a, ⊆ )$ has a finite or infinite family of minimal forbidden subgraphs.},
author = {Ewa Drgas-Burchardt},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {hereditary property; lattice of additive hereditary graph properties; minimal forbidden subgraph family; join in the lattice; minimal forbidden graph; lattice operation},
language = {eng},
number = {3},
pages = {413-418},
title = {A note on joins of additive hereditary graph properties},
url = {http://eudml.org/doc/270690},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Ewa Drgas-Burchardt
TI - A note on joins of additive hereditary graph properties
JO - Discussiones Mathematicae Graph Theory
PY - 2006
VL - 26
IS - 3
SP - 413
EP - 418
AB - Let $L^a$ denote a set of additive hereditary graph properties. It is a known fact that a partially ordered set $(L^a, ⊆ )$ is a complete distributive lattice. We present results when a join of two additive hereditary graph properties in $(L^a, ⊆ )$ has a finite or infinite family of minimal forbidden subgraphs.
LA - eng
KW - hereditary property; lattice of additive hereditary graph properties; minimal forbidden subgraph family; join in the lattice; minimal forbidden graph; lattice operation
UR - http://eudml.org/doc/270690
ER -

References

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  1. [1] A.J. Berger, Minimal forbidden subgraphs of reducible graph properties, Discuss. Math. Graph Theory 21 (2001) 111-117, doi: 10.7151/dmgt.1136. Zbl0989.05060
  2. [2] A.J. Berger, I. Broere, S.J.T. Moagi and P. Mihók, Meet- and join-irreducibility of additive hereditary properties of graphs, Discrete Math. 251 (2002) 11-18, doi: 10.1016/S0012-365X(01)00323-5. Zbl1003.05101
  3. [3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: V.R. Kulli, ed., Advances in Graph Theory (Vishawa International Publication, Gulbarga, 1991) 41-68. 
  4. [4] I. Broere, M. Frick and G.Semanišin, Maximal graphs with respect to hereditary properties, Discuss. Math. Graph Theory 17 (1997) 51-66, doi: 10.7151/dmgt.1038. Zbl0902.05027
  5. [5] D.L. Greenwell, R.L. Hemminger and J. Klerlein, Forbidden subgraphs, Proceedings of the 4th S-E Conf. Combinatorics, Graph Theory and Computing (Utilitas Math., Winnipeg, Man., 1973) 389-394. Zbl0312.05128
  6. [6] J. Jakubik, On the Lattice of Additive Hereditary Properties of Finite Graphs, Discuss. Math. General Algebra and Applications 22 (2002) 73-86. Zbl1032.06003

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