Abstract
A notion of anin-tree is introduced. It is then used to characterize and count plane embeddings of outerplanar graphs. In-trees have also been applied in the study of independent vertex covers of faces in outerplanar graphs.
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References
A. Proskurowski and M. M. Sysło,Minimum dominating cycles in outerplanar graphs, Internat. J. Comput. Inform. Sci. 10 (1981) 127–139.
M. M. Sysło,Independent face and vertex covers in plane graphs, TR N-184, Institute of Computer Science, University of Wrocław, 1987 (to appear in the Proceedings of the Banach Center, PWN, Warsaw).
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P. Winter and M. M. Sysło,Outerplanar graphs with perfect face-independent vertex covers, Technical Report, Institute of Datalogy, University of Copenhagen, 1988.
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This research was partially supported by the grant RP.I.09, from the Institute of Informatics, University of Warsaw. Hospitality of the Institute of Datalogy, University of Copenhagen where this research has been completed is gratefully acknowledged.