Indexed by:
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:
Reprint 's Address:
Email:
Version:
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:
SCOPUS Cited Count:
ESI Highly Cited Papers on the List: 0 Unfold All
WanFang Cited Count:
Chinese Cited Count:
30 Days PV: 1
Affiliated Colleges: