Discussiones Mathematicae Graph Theory 17(1) (1997)
137-145
DOI: https://doi.org/10.7151/dmgt.1047
GENERALIZED COLORINGS AND AVOIDABLE ORIENTATIONS
Jenö Szigeti Mathematical Institute, University of Miskolc |
Zsolt Tuza Computer and Automation Institute |
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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