DMGT

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ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 19(2) (1999) 159-166
DOI: https://doi.org/10.7151/dmgt.1092

REMARKS ON THE EXISTENCE OF UNIQUELY PARTITIONABLE PLANAR GRAPHS

Mieczysław Borowiecki

Institute of Mathematics
Technical University Zielona Góra, Poland
e-mail: m.borowiecki@im.uz.zgora.pl

Peter Mihók

Faculty of Economics
Technical University Košice, Slovakia
e-mail: mihok@Košice.upjs.sk

Zsolt Tuza

Computer and Automation Institute
Hungarian Academy of Sciences Budapest, Hungary

e-mail: tuza@lutra.sztaki.hu

M. Voigt

Institute of Mathematics
Technical University Ilmenau, Germany
e-mail: voigt@mathematik.tu-ilmenau.de

Abstract

We consider the problem of the existence of uniquely partitionable planar graphs. We survey some recent results and we prove the nonexistence of uniquely (D1,D1)-partitionable planar graphs with respect to the property D1 "to be a forest".

Keywords: property of graphs, additive, hereditary, vertex partition, uniquely partitionable graphs.

1991 Mathematics Subject Classification: 05C15, 05C35, O5C75.

References

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Received 2 February 1999
Revised 21 September 1999


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