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author:

Chen, Bin (Chen, Bin.) [1] | Hou, Xinmin (Hou, Xinmin.) [2] | Yu, Gexin (Yu, Gexin.) [3] | Zhou, Xinyu (Zhou, Xinyu.) [4]

Indexed by:

SCIE

Abstract:

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).

Keyword:

Connectedness Linkedness Tournament

Community:

  • [ 1 ] [Chen, Bin]Hefei Natl Lab, Hefei 230088, Anhui, Peoples R China
  • [ 2 ] [Hou, Xinmin]Hefei Natl Lab, Hefei 230088, Anhui, Peoples R China
  • [ 3 ] [Hou, Xinmin]Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
  • [ 4 ] [Zhou, Xinyu]Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China
  • [ 5 ] [Hou, Xinmin]Univ Sci & Technol China, CAS Key Lab Wu Wen Tsun Math, Hefei 230026, Anhui, Peoples R China
  • [ 6 ] [Yu, Gexin]William & Mary, Dept Math, Williamsburg, VA USA
  • [ 7 ] [Chen, Bin]Fuzhou Univ, Sch Math & Stat, Fuzhou, Peoples R China

Reprint 's Address:

  • [Hou, Xinmin]Hefei Natl Lab, Hefei 230088, Anhui, Peoples R China;;[Hou, Xinmin]Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China;;[Hou, Xinmin]Univ Sci & Technol China, CAS Key Lab Wu Wen Tsun Math, Hefei 230026, Anhui, Peoples R China

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Source :

GRAPHS AND COMBINATORICS

ISSN: 0911-0119

Year: 2025

Issue: 5

Volume: 41

0 . 6 0 0

JCR@2023

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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