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author:

Chen, Bin (Chen, Bin.) [1] (Scholars:陈彬)

Indexed by:

EI Scopus SCIE

Abstract:

In this paper, we give two extremal results on vertex disjoint-directed cycles in tournaments and bipartite tournaments. Let q >= 2 $q\ge 2$ and k >= 2 $k\ge 2$ be two integers. The first result is that for every strong tournament D $D$, with a minimum out-degree of at least (q-1)k-1 $(q-1)k-1$ with q >= 3 $q\ge 3$, any k $k$ vertex disjoint-directed cycle, which has a length of at least q $q$ in D $D$, has the same length if and only if q=3,k=2 $q=3,k=2$ and D $D$ is isomorphic to PT7 $P{T}_{7}$. The second result is that for each strong bipartite tournament D $D$, with a minimum out-degree of at least qk-1 $qk-1$ with q $q$ being even, any k $k$ vertex disjoint-directed cycle, each of which has a length of at least 2q $2q$ in D $D$, has the same length if and only if D $D$ is isomorphic to a member of BT(n1,n2,& mldr;,nqk) $BT({n}_{1},{n}_{2},\ldots ,{n}_{qk})$. Our results generalize some results of Tan and of Chen and Chang, and in a sense, extend several results of Bang-Jensen et al. of Ma et al. as well as of Wang et al.

Keyword:

bipartite tournament disjoint cycle tournament

Community:

  • [ 1 ] [Chen, Bin]Fuzhou Univ, Sch Math & Stat, Fuzhou, Fujian, Peoples R China
  • [ 2 ] [Chen, Bin]Hefei Natl Lab, Hefei, Peoples R China

Reprint 's Address:

  • 陈彬

    [Chen, Bin]Fuzhou Univ, Sch Math & Stat, Fuzhou, Fujian, Peoples R China;;[Chen, Bin]Hefei Natl Lab, Hefei, Peoples R China

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Source :

JOURNAL OF GRAPH THEORY

ISSN: 0364-9024

Year: 2025

Issue: 1

Volume: 110

Page: 111-121

0 . 9 0 0

JCR@2023

CAS Journal Grade:2

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: 1

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