# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2017-2018): c. 84%

# Discussiones Mathematicae Graph Theory

## 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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