2020/06/11 by Ruixia Wang, Hui Zhang, Wang, Ruixia +1
Engineering · Mathematics · #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Rings, Modules, and Algebras #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2006.06333
openalex publication_date 2020/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let k be an integer with k≥ 2. A digraph D is k-quasi-transitive, if for any path x0x1… xk of length k, x0 and xk are adjacent. Suppose that there exists a path of length at least k+2 in D. Let P be a shortest path of length k+2 in D. Wang and Zhang [Hamiltonian paths in k-quasi-transitive digraphs, Discrete Mathematics, 339(8) (2016) 2094--2099] proved that if k is even and k≥ 4, then D[V(P)] and D[V(D)∖ V(P)] are both semicomplete digraphs. In this paper, we shall prove that if k is odd and k≥ 5, then D[V(P)] is either a semicomplete digraph or a semicomplete bipartite digraph and D[V(D)∖ V(P)] is either a semicomplete digraph, a semicomplete bipartite digraph or an empty digraph.