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- W4366155343 abstract "Let G be a 2-connected balanced bipartite graph of order 2n with n≥3. Denote μ(G)=min{max{d(x),d(y)}:x,y∈V(G),dist(x,y)=2} and μ2(G)=min{d(x)+d(y):x,y∈V(G),dist(x,y)=2}. Wang and Liu (2018) [14] proved that if μ(G)≥n+12, then G is hamiltonian. In this paper, we characterize non-hamiltonian bipartite graphs with μ(G)=n2. Also, we show that G is bipancyclic with one exception, if μ(G)≥n+12. As a direct consequence, we also show that if μ2(G)≥n+1, then G is hamiltonian and, with one exception, G is bipancyclic. Moreover, if we replace n+1 with n+2, then G contains a hamiltonian cycle passing through every edge of a perfect matching. The lower bounds in all results are sharp." @default.
- W4366155343 created "2023-04-19" @default.
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- W4366155343 date "2023-07-01" @default.
- W4366155343 modified "2023-10-15" @default.
- W4366155343 title "Degree sum condition on distance 2 vertices for hamiltonian cycles in balanced bipartite graphs" @default.
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- W4366155343 doi "https://doi.org/10.1016/j.disc.2023.113446" @default.
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