Abstract
Two important branches of graph connectivity problems are connectivity augmentation, which consists of augmenting a graph by adding new edges so as to meet a specified target connectivity, and connectivity orientation, where the goal is to find an orientation of an undirected or mixed graph that satisfies some specified edge-connection property. In the present work an attempt is made to link the above two branches, by considering degree-specified and minimum cardinality augmentation of graphs so that the resulting graph has an orientation satisfying a prescribed edge-connection requirement, such as (k, l)-edge- connectivity. Our proof technique involves a combination of the super- modular polyhedral methods used in connectivity orientation, and the splitting off operation, which is a standard tool in solving augmentation problems.
Supported by the Hungarian National Foundation for Scientific Research, OTKA T029772. Part of research was done while this author was visiting the Institute for Discrete Mathematics, University of Bonn, July 2000.
Supported by the Hungarian National Foundation for Scientific Research, OTKA T029772.
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Frank, A., Király, T. (2001). Combined Connectivity Augmentation and Orientation Problems. In: Aardal, K., Gerards, B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2001. Lecture Notes in Computer Science, vol 2081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45535-3_11
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DOI: https://doi.org/10.1007/3-540-45535-3_11
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