k-strong spanning local tournaments in locally semicomplete digraphs

Authors:
Jørgen Bang-Jensen
Affiliations:
Department of Maths and Computer Science, University of Southern Denmark, DK-5230,Odense, Denmark
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 8
Cited 0

Locally semicomplete digraphs: a generalization of tournaments

Journal of Graph Theory
Configurations in graphs of large minimum degree, connectivity, or chromatic number

Proceedings of the third international conference on Combinatorial mathematics
Connectivity properties of locally semicomplete digraphs

Journal of Graph Theory
On the structure of local tournaments

Journal of Combinatorial Theory Series B
Spanning local tournaments in locally semicomplete digraphs

Proceedings of the 4th Twente workshop on Graphs and combinatorial optimization
A note on spanning local tournaments in locally semicomplete digraphs

Discrete Applied Mathematics
Linkages in locally semicomplete digraphs and quasi-transitive digraphs

Discrete Mathematics
Digraphs: Theory, Algorithms and Applications

Digraphs: Theory, Algorithms and Applications

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Abstract

We point out mistakes in two papers previously published in Discrete Applied Mathematics, dealing with highly strongly connected spanning local tournaments in locally semicomplete digraphs. We conjecture that every (2k-1)-strong locally semicomplete digraph on at least 2k+1 vertices contains a k-strong spanning local tournament and prove the conjecture for k=1,2. We also prove that every 5-strong locally semicomplete digraph which is not semicomplete contains a 3-strong spanning local tournament. We furthermore show that for semicomplete digraphs, which form a proper subclass of locally semicomplete digraphs, 2k-1 would be the best possible bound and for locally semicomplete digraphs which are not semicomplete we show that the correct bound is at least 2k-3.