On varieties of graphs
Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 2, pp. 209-223.

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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.
Keywords: graph, subgraph identification, variety
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Haviar, Alfonz; Nedela, Roman. On varieties of graphs. Discussiones Mathematicae. Graph Theory, Tome 18 (1998) no. 2, pp. 209-223. http://geodesic.mathdoc.fr/item/DMGT_1998_18_2_a7/

[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.

[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] S. Burris and H.P. Sankappanavar, A Course in Universal Algebra (Springer-Verlag, New York, Heidelberg, Berlin, 1981).

[4] G. Chartrand and L. Lesniak, Graphs Digraphs, (third ed.) (Chapman Hall, London, 1996).

[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] 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] S. Klavžar and M. Petkovšek, Notes on hereditary classes of graphs, Preprint Ser. Dept. Math. University E.K., Ljubljana, 25 (1987) 206.

[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] E.R. Scheinerman, On the structure of hereditary classes of graphs, Jour. Graph Theory 10 (1986) 545-551, doi: 10.1002/jgt.3190100414.

[10] C. Thomassen, Embeddings and minors, in: Handbook of combinatorics, R. Graham, M. Grötsches and L. Lovász, eds. (Elesevier Science B.V., 1965).