On varieties of graphs

Alfonz Haviar; Roman Nedela

Discussiones Mathematicae Graph Theory (1998)

  • Volume: 18, Issue: 2, page 209-223
  • ISSN: 2083-5892

Abstract

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In this paper, we introduce the notion of a variety of graphs closed under isomorphic images, subgraph identifications and induced subgraphs (induced connected subgraphs) firstly and next closed under isomorphic images, subgraph identifications, circuits and cliques. The structure of the corresponding lattices is investigated.

How to cite

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Alfonz Haviar, and Roman Nedela. "On varieties of graphs." Discussiones Mathematicae Graph Theory 18.2 (1998): 209-223. <http://eudml.org/doc/270513>.

@article{AlfonzHaviar1998,
abstract = {In this paper, we introduce the notion of a variety of graphs closed under isomorphic images, subgraph identifications and induced subgraphs (induced connected subgraphs) firstly and next closed under isomorphic images, subgraph identifications, circuits and cliques. The structure of the corresponding lattices is investigated.},
author = {Alfonz Haviar, Roman Nedela},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph; subgraph identification; variety; variety of graphs; subgraph identifications},
language = {eng},
number = {2},
pages = {209-223},
title = {On varieties of graphs},
url = {http://eudml.org/doc/270513},
volume = {18},
year = {1998},
}

TY - JOUR
AU - Alfonz Haviar
AU - Roman Nedela
TI - On varieties of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 1998
VL - 18
IS - 2
SP - 209
EP - 223
AB - In this paper, we introduce the notion of a variety of graphs closed under isomorphic images, subgraph identifications and induced subgraphs (induced connected subgraphs) firstly and next closed under isomorphic images, subgraph identifications, circuits and cliques. The structure of the corresponding lattices is investigated.
LA - eng
KW - graph; subgraph identification; variety; variety of graphs; subgraph identifications
UR - http://eudml.org/doc/270513
ER -

References

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  1. [1] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discusiones Mathematicae Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037. Zbl0902.05026
  2. [2] 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. 
  3. [3] S. Burris and H.P. Sankappanavar, A Course in Universal Algebra (Springer-Verlag, New York, Heidelberg, Berlin, 1981). Zbl0478.08001
  4. [4] G. Chartrand and L. Lesniak, Graphs & Digraphs, (third ed.) (Chapman & Hall, London, 1996). Zbl0890.05001
  5. [5] D. Duffus and I. Rival, A Structure Theory for Ordered Sets, Discrete Math. 35 (1981) 53-118, doi: 10.1016/0012-365X(81)90201-6. 
  6. [6] R.P. Jones, Hereditary properties and P-chromatic numbers, in: Combinatorics, Proc. British Combin. Conf., Aberystwyth 1973, T.P. McDonough and V.C. Mavron, eds. (Cambridge Univ. Press, Cambridge, 1974) 83-88. 
  7. [7] S. Klavžar and M. Petkovšek, Notes on hereditary classes of graphs, Preprint Ser. Dept. Math. University E.K., Ljubljana, 25 (1987) 206. 
  8. [8] P. Mihók, On graphs critical with respect to generalized independence numbers, in: Colloquia Mathematica Societatis János Bolyai 52, Combinatorics 2 (1987) 417-421. 
  9. [9] E.R. Scheinerman, On the structure of hereditary classes of graphs, Jour. Graph Theory 10 (1986) 545-551, doi: 10.1002/jgt.3190100414. Zbl0609.05057
  10. [10] C. Thomassen, Embeddings and minors, in: Handbook of combinatorics, R. Graham, M. Grötsches and L. Lovász, eds. (Elesevier Science B.V., 1965). 

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