Decomposing locally semicomplete digraphs into strong spanning subdigraphs

  • Authors:

  • Jørgen Bang-Jensen;Jing Huang

  • Affiliations:

  • Department of Mathematics and Computer Science, University of Southern Denmark, DK-5230, Odense, Denmark;Department of Mathematics and Statistics, University of Victoria, PO BOX 3060 STN CSC, Victoria, B.C., V8W 3R4, Canada

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

We prove that the arc set of every 2-arc-strong locally semicomplete digraph D=(V,A) which is not the second power of an even cycle can be partitioned into two sets A"1,A"2 such that both of the spanning subdigraphs D"1=(V,A"1) and D"2=(V,A"2) are strongly connected. Moreover, we show that such a partition (if it exists) can be obtained in polynomial time. This generalizes a result from Bang-Jensen and Yeo (2004) [5] on semicomplete digraphs and implies that every 2-arc-strong locally semicomplete digraph D=(V,A) has a pair of arc-disjoint branchings B"u^-,B"v^+ such that B"u^- is an in-branching rooted at u and B"v^+ is an out-branching rooted at v where u,v@?V can be chosen arbitrarily. This generalizes results from Bang-Jensen (1991) [2] for tournaments and Bang-Jensen and Yeo (2004) [5] for semicomplete digraphs.