Discussiones
Mathematicae Graph Theory 19(2) (1999) 199-217
DOI: https://doi.org/10.7151/dmgt.1095
GENERALIZED RAMSEY THEORY AND DECOMPOSABLE PROPERTIES OF GRAPHS
Stefan A. Burr Department of Computer Science |
Michael S. Jacobson University of Louisville |
Peter Mihók Mathematical Institute, Slovak Academy of Sciences |
Gabriel Semanišin Department of Geometry and Algebra |
Abstract
In this paper we translate Ramsey-type problems into the language of decomposable hereditary properties of graphs. We prove a distributive law for reducible and decomposable properties of graphs. Using it we establish some values of graph theoretical invariants of decomposable properties and show their correspondence to generalized Ramsey numbers.
Keywords: hereditary properties, additivity, reducibility, decomposability, Ramsey number, graph invariants.
1991 Mathematics Subject Classification: 05C15, 05C55, 05C75.
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Received 2 February 1999
Revised 8 September 1999
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