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Cubo (Temuco)

On-line version ISSN 0719-0646

Cubo vol.24 no.2 Temuco Aug. 2022 


Perfect matchings in inhomogeneous random bipartite graphs in random environment

1Department of Mathematics, The Pennsylvania State University, USA.

2Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile.

3Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile.


In this note we study inhomogeneous random bipartite graphs in random environment. These graphs can be thought of as an extension of the classical Erdös-Rényi random bi-partite graphs in a random environment. We show that the expected number of perfect matchings obeys a precise asymptotic.

Keywords and Phrases: Perfect matchings; large permanents; random graphs


En esta nota estudiamos grafos aleatorios bipartitos inhomogéneos en un ambiente aleatorio. Estos grafos pueden ser pensados como una extensión de los grafos bipartitos aleatorios clásicos de Erdös-Rényi en un ambiente aleatorio. Mostramos que el número esperado de pareos obedece un comportamiento asintótico preciso.

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The authors were partially supported by CONICYT PIA ACT172001. J.B. was partially supported by Proyecto Fondecyt 1180371. G.I. was partially supported by Fondecyt 1190194. M.P. was partially supported by Fondecyt 1180922.


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Accepted: April 13, 2022; Received: October 15, 2021

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