DMGT

Discussiones Mathematicae Graph Theory 17(1) (1997) 77-88
DOI: https://doi.org/10.7151/dmgt.1040

GRAPHS MAXIMAL WITH RESPECT TO HOM-PROPERTIES

Jan Kratochvíl

Department of Applied Mathematics
Charles University
Malostranské nám. 25, 118 00 Praha 1, Czech Republic
e-mail: honza@kam.ms.mff.cuni.cz

Peter Mihók

Mathematical Institute
Slovak Academy of Sciences
Grešákova 6, 040 01 Košice, Slovak Republic
e-mail: mihok@Košice.upjs.sk

Gabriel Semanišin

Department of Geometry and Algebra
Faculty of Science, P. J. Šafárik University
Jesenná 5, 041 54 Košice, Slovak Republic
e-mail: semanisin@duro.upjs.sk

Abstract

For a simple graph H, →H denotes the class of all graphs that admit homomorphisms to H (such classes of graphs are called hom-properties). We investigate hom-properties from the point of view of the lattice of hereditary properties. In particular, we are interested in characterization of maximal graphs belonging to →H. We also provide a description of graphs maximal with respect to reducible hom-properties and determine the maximum number of edges of graphs belonging to →H.

Keywords: hom-property of graphs, hereditary property of graphs, maximal graphs.

1991 Mathematics Subject Classification: 05C15, 05C35, 05C75.

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