An orientation theorem with parity conditions

András Frank, Tibor Jordán, Zoltán Szigeti

Research output: Contribution to journalArticle

11 Citations (Scopus)


Given a graph G=(V,E) and a set T⊆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.

Original languageEnglish
Pages (from-to)37-47
Number of pages11
JournalDiscrete Applied Mathematics
Issue number1-3
Publication statusPublished - Nov 15 2001

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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