DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

Discussiones Mathematicae Graph Theory

PDF

Discussiones Mathematicae Graph Theory 21(1) (2001) 207-221
DOI: 10.7151/dmgt.1144

ON VARIETIES OF ORGRAPHS

Alfonz Haviar and Gabriela Monoszová

Department of Mathematics, Faculty of Natural Sciences
Matej Bel University, Tajovského 40, 974 01
Banská Bystrica, Slovakia
e-mail: haviar.umb.sk
e-mail: monosz.umb.sk

Abstract

In this paper we investigate varieties of orgraphs (that is, oriented graphs) as classes of orgraphs closed under isomorphic images, suborgraph identifications and induced suborgraphs, and we study the lattice of varieties of tournament-free orgraphs.

Keywords: orgraph, variety, lattice.

2000 Mathematics Subject Classification: 05C20.

References

[1] B. Bollobás, Extremal Graph Theory (Academic press, London, New York, San Francisco, 1978).
[2] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semani sin, A 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 Inter. Publ., Gulbarga, 1991) 41-68.
[4] S. Buris and H.P. Sankappanavar, A Course in Universal Algebra (Springer-Verlag, New York, Heidelberg, Berlin, 1981).
[5] G. Chartrand, O.R. Oellermann, Applied and Algorithmic Graph Theory (Mc Graw-Hill, 1993).
[6] R. Diestel, Graph Theory (Springer-Verlag New York, 1997).
[7] 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.
[8] A. Haviar and R. Nedela, On varieties of graphs, Discuss. Math. Graph Theory 18 (1998) 209-223, doi: 10.7151/dmgt.1077.
[9] A. Haviar, The lattice of varieties of graphs, Acta Univ. M. Belii, ser. Math. 8 (2000) 11-19.
[10] P. Mihók and R. Vasky, Hierarchical Decompositions of Diagrams in Information System Analysis and Lattices of Hereditary Properties of Graphs, Proceedings of ISCM Herlany 1999, ed. A. Has cák, V. Pirc, V. Soltés (University of Technology, Košice, 2000) 126-129.
[11] E.R. Scheinerman, On the structure of hereditary classes of graphs, J. Graph Theory 10 (1986) 545-551.

Received 13 November 2000
Revised 16 May 2001