Wang, Ruixia; Wu, Linxin A dominating pair condition for a balanced bipartite digraph to be Hamiltonian. (English) Zbl 1447.05093 Australas. J. Comb. 77, Part 1, 136-143 (2020). In a digraph, a vertex \(x\) is said to dominate vertex \(y\) if there is an arc from \(x\) to \(y\). Similarly, a vertex \(z\) is said to dominate vertices \(x\) and \(y\) if \(z\) dominates both \(x\) and \(y\). Likewise, the pair of vertices \(x\) and \(y\) dominates \(z\) if both \(x\) and \(y\) dominate \(z\). [the first author, Discrete Math. Theor. Comput. Sci. 19, No. 3, Paper No. 11, 12 p. (2017; Zbl 1401.05177)] gave a dominating pair sufficient condition for Hamiltonicity of a balanced bipartite digraph. In the present paper, it is shown that a strong balanced bipartite digraph of order \(2a\) contains a Hamiltonian cycle if for every dominating pair of vertices \(x\) and \(y\), their degrees \(d(x)\) and \(d(y)\) satisfy certain degree inequalities involving \(a\). Reviewer: Wai-Kai Chen (Fremont) Cited in 4 Documents MSC: 05C20 Directed graphs (digraphs), tournaments 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C45 Eulerian and Hamiltonian graphs Keywords:bipartite digraph; dominating pair condition; Hamiltonicity; degree Citations:Zbl 1401.05177 PDFBibTeX XMLCite \textit{R. Wang} and \textit{L. Wu}, Australas. J. Comb. 77, Part 1, 136--143 (2020; Zbl 1447.05093) Full Text: Link References: [1] J. Adamus, A degree sum condition for hamiltonicity in balanced bipartite digraphs,Graphs Combin.33 (2017), 43-51. · Zbl 1365.05163 [2] J. Adamus, A Meyniel-Type condition for bipancyclicity in balanced bipartite digraphs,Graphs Combin.34 (2018), 703-709. · Zbl 1395.05065 [3] J. Adamus and L. Adamus, A degree condition for cycles of maximum length in bipartite digraphs,Discrete Math.312 (2012), 1117-1122. · Zbl 1238.05149 [4] J. Adamus, L. Adamus and A. Yeo, On the Meyniel condition for hamiltonicity in bipartite digraphs,Discrete Math. Theor. Comput. Sci.16 (2014), 293-302. · Zbl 1294.05081 [5] J. Bang-Jensen, Y. Guo and A. Yeo, A new sufficient condition for a digraph to be Hamiltonian,Discrete Appl. Math.95 (1999), 61-72. · Zbl 0933.05095 [6] J. Bang-Jensen and G. Gutin, Digraphs: Theory, Algorithms and Applications, Springer, London, 2000. · Zbl 1001.05002 [7] J. Bang-Jensen, G. Gutin and H. Li, Sufficient conditions for a digraph to be Hamiltonian,J. Graph Theory22(2) (1996), 181-187. · Zbl 0854.05067 [8] H. Meyniel, Une condition suffisante d’existence d’un circuit hamiltonien dans un graphe orient´e,J. Combin. Theory Ser. B14 (1973), 137-147. · Zbl 0259.05114 [9] R. Wang, A sufficient condition for a balanced bipartite digraph to be hamiltonian,Discrete Math. Theor. Comput. Sci.19(3) (2017), #11. · Zbl 1401.05177 [10] R. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.