Extremal Planar Matchings of Inhomogenous Random Bipartite Graphs

Ghurumuruhan Ganesan ()
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Ghurumuruhan Ganesan: University of Bristol

Sankhya A: The Indian Journal of Statistics, 2025, vol. 87, issue 1, No 6, 134-156

Abstract: Abstract In this paper we study maximum size and minimum weight planar matchings of inhomogenous random bipartite graphs. Our motivation for this study comes from efficient usage of cross edges in relay networks for overall improvement in network performance. We first consider Bernoulli planar matchings with a constraint on the edge length and obtain deviation estimates for the maximum size of a planar matching. We then equip each edge of the complete bipartite graph with a positive random weight and obtain bounds on the minimum weight of a planar matching containing a given number of edges. We also use segmentation and martingale methods to obtain $$L^2-$$ L 2 - convergence of the minimum weight, appropriately scaled and centred.

Keywords: Length constrained planar matchings; minimum weight planar matchings; weight saturation; Primary:; 60C05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13171-024-00374-6

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