TY - JOUR
T1 - Note on disjoint cycles in multipartite tournaments
AU - Gutin, Gregory
AU - Li, Wei
AU - Wang, Shujing
AU - Yeo, Anders
AU - Zhou, Yacong
PY - 2024/10
Y1 - 2024/10
N2 - In 1981, Bermond and Thomassen conjectured that for any positive integer k, every digraph with minimum out-degree at least 2k−1 admits k vertex-disjoint directed cycles. In this short paper, we verify the Bermond-Thomassen conjecture for triangle-free multipartite tournaments and 3-partite tournaments. Furthermore, we characterize 3-partite tournaments with minimum out-degree at least 2k−1 (k≥2) such that in each set of k vertex-disjoint directed cycles, every cycle has the same length.
AB - In 1981, Bermond and Thomassen conjectured that for any positive integer k, every digraph with minimum out-degree at least 2k−1 admits k vertex-disjoint directed cycles. In this short paper, we verify the Bermond-Thomassen conjecture for triangle-free multipartite tournaments and 3-partite tournaments. Furthermore, we characterize 3-partite tournaments with minimum out-degree at least 2k−1 (k≥2) such that in each set of k vertex-disjoint directed cycles, every cycle has the same length.
KW - Bermond-Thomassen conjecture
KW - Disjoint cycles
KW - Minimum out-degree
KW - Multipartite tournaments
U2 - 10.1016/j.disc.2024.114126
DO - 10.1016/j.disc.2024.114126
M3 - Journal article
AN - SCOPUS:85195660040
SN - 0012-365X
VL - 347
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 10
M1 - 114126
ER -