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A digraph D is k-linked if for any pair of two disjoint vertex sets {x(1), x(2),..., x(k)} and {y(1), y(2),..., y(k)} in D, there exist vertex disjoint dipaths P-1, P-2,..., P-k such that P-i is a dipath from x(i) to y(i) for each i is an element of [k]. Pokrovskiy (JCTB, 2015) confirmed a conjecture of Kuhn et al. (Proc. Lond. Math. Soc., 2014) by verifying that every 452k-connected tournament is k-linked. Meng et al. (Eur. J. Comb., 2021) improved this upper bound by showing that any (40k- 31)-connected tournament is k-linked. In this paper, we show a better upper bound by proving that every inverted right perpendicular 12.5k- 6 inverted left perpendicular-connected tournament with minimum out-degree at least 21k - 14 is k-linked. Furthermore, we improve a key lemma that was first introduced by Pokrovskiy (JCTB, 2015) and later enhanced by Meng et al. (Eur. J. Comb., 2021).
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GRAPHS AND COMBINATORICS
ISSN: 0911-0119
Year: 2025
Issue: 5
Volume: 41
0 . 6 0 0
JCR@2023
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ESI Highly Cited Papers on the List: 0 Unfold All
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30 Days PV: 0
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