DMGT

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
City College, C.U.N.Y. New York, NY 10031, U.S.A.
e-mail: burr@cs-mail.engr.ccny.cuny.edu

Michael S. Jacobson

University of Louisville
Louisville, KY 40292, U.S.A.
e-mail: mikej@luisville.edu

Peter Mihók

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

Gabriel Semanišin

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

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.

References

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Received 2 February 1999
Revised 8 September 1999