Graphs maximal with respect to hom-properties

• Autorzy: Jan Kratochvíl , Peter Mihók , Gabriel Semanišin
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hom-property of graphs; hereditary property of graphs; maximal graphs

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C35: Extremal problems
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1997
• Tom: 17
• Numer: 1
• Strony: 77-88

Daty

wydano

1997

otrzymano

1997-01-03

poprawiono

1997-04-01

Twórcy

autor

Jan Kratochvíl

• Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic

autor

Peter Mihók

• Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01 Košice, Slovak Republic

autor

Gabriel Semanišin

• Department of Geometry and Algebra, Faculty of Science, P. J. Šafárik University, Jesenná 5, 041 54 Košice, Slovak Republic

Bibliografia

• [1] M. Borowiecki and P. Mihók, Hereditary Properties of Graphs, in: Advances in Graph Theory (Vishwa International Publications, 1991) 41-68.
• [2] I. Broere, M. Frick and G. Semanišin, Maximal graphs with respect to hereditary properties, Discussiones Mathematicae Graph Theory 17 (1997) 51-66, doi: 10.7151/dmgt.1038.
• [3] R.L. Graham, M. Grötschel and L. Lovász, Handbook of Combinatorics (Elsevier Science B.V. Amsterdam, 1995).
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• [5] P. Hell and J. Nešetril, Complexity of H-coloring, J. Combin. Theory (B) 48 (1990) 92-110, doi: 10.1016/0095-8956(90)90132-J.
• [6] T.R. Jensen and B. Toft, Graph Colouring Problems (Wiley-Interscience Publications New York, 1995).
• [7] J. Kratochví l and P. Mihók, Hom-properties are uniquely factorizable into irreducible factors (submitted).
• [8] P. Mihók and G. Semanišin, Reducible properties of graphs, Discussiones Math. Graph Theory 15 (1995) 11-18, doi: 10.7151/dmgt.1002.
• [9] P. Mihók and G. Semanišin, On the chromatic number of reducible hereditary properties (submitted).
• [10] J. Nešetril, Graph homomorphisms and their structures, in: Proc. Seventh Quadrennial International Conference on the Theory and Applications of Graphs 2 (1995) 825-832.
• [11] M. Simonovits, Extremal graph theory, in: L.W. Beineke and R.J. Wilson, eds., Selected Topics in Graph Theory vol. 2, (Academic Press, London, 1983) 161-200.
• [12] X. Zhou, Uniquely H-colourable graphs with large girth, J. Graph Theory 23 (1996) 33-41, doi: 10.1002/(SICI)1097-0118(199609)23:1<33::AID-JGT3>3.0.CO;2-L

Identyfikatory

DOI

10.7151/dmgt.1040