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Dirac-type Theorems for Inhomogenous Random Graphs

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  • Ghurumuruhan Ganesan

    (IISER Bhopal)

Abstract

In this paper, we study Dirac-type theorems for an inhomogenous random graph $$G$$ G whose edge probabilities are not necessarily all the same. We obtain sufficient conditions for the existence of Hamiltonian paths and perfect matchings, in terms of the sum of edge probabilities. For edge probability assignments with two-sided bounds, we use Pósa rotation and single vertex exclusion techniques to show that $$G$$ G is Hamiltonian with high probability. For weaker one-sided bounds, we use bootstrapping techniques to obtain a perfect matching in $$G,$$ G , with high probability. We also highlight an application of our results in the context of channel assignment problem in wireless networks.

Suggested Citation

  • Ghurumuruhan Ganesan, 2024. "Dirac-type Theorems for Inhomogenous Random Graphs," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 775-789, August.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:2:d:10.1007_s13171-024-00353-x
    DOI: 10.1007/s13171-024-00353-x
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    1. Ganesan, Ghurumuruhan, 2020. "Extremal paths in inhomogenous random graphs," Statistics & Probability Letters, Elsevier, vol. 156(C).
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