Abstract
Given a graph G = (V, E) and a set \( T \subseteq V\), an orientation of G is called T-odd if precisely the vertices of T get odd in-degree. We give a good characterization for the existence of a T-odd orientation for which there exist k edge-disjoint spanning arborescences rooted at a prespecified set of k roots. Our result implies Nash-Williams’ theorem on covering the edges of a graph by k forests and a (generalization of a) theorem due to Nebeský on upper embeddable graphs.
Supported by the Hungarian National Foundation for Scientific Research Grant OTKA T029772.
Supported in part by the Danish Natural Science Research Council, grant no. 28808.
Basic Research in Computer Science, Centre of the Danish National Research Foundation.
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© 1999 Springer-Verlag Berlin Heidelberg
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Frank, A., Jordán, T., Szigeti, Z. (1999). An Orientation Theorem with Parity Conditions. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1999. Lecture Notes in Computer Science, vol 1610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48777-8_14
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DOI: https://doi.org/10.1007/3-540-48777-8_14
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