DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory  17(1) (1997)   137-145
DOI: 10.7151/dmgt.1047

GENERALIZED COLORINGS AND AVOIDABLE ORIENTATIONS

Jenö Szigeti

Mathematical Institute, University of Miskolc
H-3515 Miskolc-Egyetemváros, Hungary

Zsolt Tuza

Computer and Automation Institute
Hungarian Academy of Sciences
H-1111 Budapest, Kende u. 13-17, Hungary

Abstract

Gallai and Roy proved that a graph is k-colorable if and only if it has an orientation without directed paths of length k. We initiate the study of analogous characterizations for the existence of generalized graph colorings, where each color class induces a subgraph satisfying a given (hereditary) property. It is shown that a graph is partitionable into at most k independent sets and one induced matching if and only if it admits an orientation containing no subdigraph from a family of k+3 directed graphs.

Keywords: hereditary property, graph coloring.

1991 Mathematics Subject Classification: 05C15, 05C75.

References

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