Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
419706 | Discrete Applied Mathematics | 2009 | 5 Pages |
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)(2k−1)-strong locally semicomplete digraph on at least 2k+12k+1 vertices contains a kk-strong spanning local tournament and prove the conjecture for k=1,2k=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−12k−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−32k−3.