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Extremal paths in inhomogenous random graphs

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  • Ganesan, Ghurumuruhan

Abstract

In this paper, we study long open paths in an inhomogenous Erdős–Rényi random graph G obtained from the complete graph Kn on n vertices by allowing each edge e to be open with probability pn(e), independently of other edges. If the edge probability assignment sequence satisfies certain neighbour density conditions, then G has a long path containing nearly all the vertices with high probability, i.e., with probability converging to one as n→∞. Our methods extend to random weighted graphs with nonidentical weight distributions and we describe conditions under which the minimum weight Hamiltonian path has weight bounded above by a constant, with high probability.

Suggested Citation

  • Ganesan, Ghurumuruhan, 2020. "Extremal paths in inhomogenous random graphs," Statistics & Probability Letters, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:stapro:v:156:y:2020:i:c:s0167715219302391
    DOI: 10.1016/j.spl.2019.108593
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    Cited by:

    1. 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.

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