On varieties of graphs

• Autorzy: Alfonz Haviar , Roman Nedela
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

graph; subgraph identification; variety

Kategorie tematyczne

• 05C99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1998
• Tom: 18
• Numer: 2
• Strony: 209-223

Daty

wydano

1998

otrzymano

1998-01-05

poprawiono

1998-04-02

Twórcy

autor

Alfonz Haviar

• Department of Mathematics, Faculty of Science, Matej Bel University, Tajovského 40, Sk 975 49 Banská Bystrica, Slovakia

autor

Roman Nedela

• Department of Mathematics, School of Finance, Matej Bel University, Tajovského 10, Sk 974 00 Banská Bystrica, Slovakia

Bibliografia

• [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).

Identyfikatory

DOI

10.7151/dmgt.1077