Abstract
A subset U of vertices of a plane graph is said to be a perfect face-independent vertex cover (FIVC) if and only if each face has exactly one vertex in U. Necessary and sufficient conditions for a maximal plane graph to have a perfect FIVC are derived. A notion of an in-tree is used to study plane embeddings of maximal outerplanar graphs (mops) and their perfect FIVCs. Finally, a linear time algorithm which finds a minimum cardinality perfect FIVC of a mop is developed. It is argued that the results are extendable to arbitrary outerplanar graphs.
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.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
D. Bienstock and C.L. Monma, On the complexity of covering vertices by faces in a planar graph, SIAM J. on Comput. 17 (1988) 53–76.
M. Fellews, F. Hickling and M.M. Sysło, Topological parametrization and hard graph problems (extended abstract) Washington State University (1985).
M. Fellows, Personal communication (1986).
A. Proskurowski and M.M. Sysło, Minimumn dominating cycles in outerplanar graphs, Internat. J. Comput. Inform. Sci. 10 (1981) 127–139.
M.M. Sysło, On two problems related to the traveling salesman problem in Halin graphs, in: G. Hammer and D. Pallaschke (eds.), Selected Topics in Operations Research and Mathematical Economics, Lecture Notes in Economics and Math. Systems 266, Springer-Verlag, Berlin (1984) 325–335.
M.M. Sysło, Independent face and vertex covers in plane graphs, TR N-184, Institute of Computer Science, University of Wroclaw (1987).
M.M. Sysło and P. Winter, Plane embeddings of outerplanar graphs, Technical Report, Institute of Datalogy, University of Copenhagen (1988).
M.M. Sysło and P. Winter, Face-independent vertex covers of outerplanar graphs, Technical Report, Institute of Datalogy, University of Copenhagen (1988).
R.J. Wilson, Introduction to Graph Theory, Longman, London (1972).
P. Winter, Generalized Steiner problem in outerplanar graphs, BIT 25 (1985) 485–496.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1988 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Syslo, M.M., Winter, P. (1988). Independent covers in outerplanar graphs. In: Karlsson, R., Lingas, A. (eds) SWAT 88. SWAT 1988. Lecture Notes in Computer Science, vol 318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19487-8_28
Download citation
DOI: https://doi.org/10.1007/3-540-19487-8_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-19487-3
Online ISBN: 978-3-540-39288-0
eBook Packages: Springer Book Archive