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On the Hamiltonicity of random bipartite graphs

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  • Yilun Shang

    (Tongji University
    Hebrew University of Jerusalem)

Abstract

We prove that if p ≫ lnn/n, then a.a.s. every subgraph of random bipartite graph G(n, n, p) with minimum degree at least (1/2 + o(l))np is Hamiltonian. The range of p and the constant 1/2 involved are both asymptotically best possible. The result can be viewed as a generalization of the Dirac theorem within the context of bipartite graphs. The proof uses Pósa’s rotation and extension method and is closely related to a recent work of Lee and Sudakov.

Suggested Citation

  • Yilun Shang, 2015. "On the Hamiltonicity of random bipartite graphs," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(2), pages 163-173, April.
    • Handle: RePEc:spr:indpam:v:46:y:2015:i:2:d:10.1007_s13226-015-0119-6
    DOI: 10.1007/s13226-015-0119-6
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    Cited by:

    1. Guifu Su & Shuai Wang & Junfeng Du & Mingjing Gao & Kinkar Chandra Das & Yilun Shang, 2022. "Sufficient Conditions for a Graph to Be ℓ -Connected, ℓ -Deficient, ℓ -Hamiltonian and ℓ − -Independent in Terms of the Forgotten Topological Index," Mathematics, MDPI, vol. 10(11), pages 1-11, May.

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