Abstract
Let G be a connected balanced bipartite graph of order \(2n\ge 4\). Denote \(\mu _2(G)=\)min\(\{d(x)+d(y): x,y\in V(G)\), dist\((x,y)=2\}\). Some sufficient conditions for G to be hamiltonian or bipancyclic have been given in terms of vertex-degree and size of G. In this paper, we give a sufficient condition for vertex bipancyclicity of G. we show that if \(\mu _2(G)\ge n+2\), then each vertex of G is bipancyclic and the lower bound \(n+2\) is tight.
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We would like to thank the anonymous referee for many valuable suggestions that allowed us to improve the exposition of our results.
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This work is supported by the Natural Science Foundation of Shanxi Province, China (Nos. 202103021224019, 202203021211318 and 202203021221037).
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Guo, Q., Wang, R., Meng, W. et al. A Sufficient Condition for Vertex Bipancyclicity in Balanced Bipartite Graphs. Graphs and Combinatorics 39, 69 (2023). https://doi.org/10.1007/s00373-023-02668-2
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DOI: https://doi.org/10.1007/s00373-023-02668-2