Abstract
We equip the edges of a deterministic graph H with independent but not necessarily identically distributed weights and study a generalized version of matchings (i.e. a set of vertex disjoint edges) in H satisfying the property that end-vertices of any two distinct edges are at least a minimum distance apart. We call such matchings as strong matchings and determine bounds on the expectation and variance of the minimum weight of a maximum strong matching. Next, we consider an inhomogenous random graph whose edge probabilities are not necessarily the same and determine bounds on the maximum size of a strong matching in terms of the averaged edge probability. We use local vertex neighbourhoods, the martingale difference method and iterative exploration techniques to obtain our desired estimates.
Acknowledgments
I thank Professors Rahul Roy, C. R. Subramanian and the referees for crucial comments that led to an improvement of the paper. I also thank IMSc for my fellowships.
Citation
Ghurumuruhan Ganesan. "Strong and weighted matchings in inhomogenous random graphs." Electron. Commun. Probab. 26 1 - 12, 2021. https://doi.org/10.1214/21-ECP408
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